diff --git a/cpp/src/arrow/flight/sql/odbc/entry_points.cc b/cpp/src/arrow/flight/sql/odbc/entry_points.cc
index 6087eb1635f5..52ab94dd74fe 100644
--- a/cpp/src/arrow/flight/sql/odbc/entry_points.cc
+++ b/cpp/src/arrow/flight/sql/odbc/entry_points.cc
@@ -186,14 +186,7 @@ SQLRETURN SQL_API SQLCancel(SQLHSTMT stmt) {
   });
 }
 
-SQLRETURN SQL_API SQLCloseCursor(SQLHSTMT stmt) {
-  LOG_DEBUG("SQLCloseCursor called with stmt: {}", stmt);
-  return ODBC::ODBCStatement::ExecuteWithDiagnostics(stmt, SQL_ERROR, [=]() {
-    throw driver::odbcabstraction::DriverException("SQLCloseCursor is not implemented",
-                                                   "IM001");
-    return SQL_ERROR;
-  });
-}
+SQLRETURN SQL_API SQLCloseCursor(SQLHSTMT stmt) { return arrow::SQLCloseCursor(stmt); }
 
 SQLRETURN SQL_API SQLColAttribute(SQLHSTMT stmt, SQLUSMALLINT recordNumber,
                                   SQLUSMALLINT fieldIdentifier,
diff --git a/cpp/src/arrow/flight/sql/odbc/odbc_api.cc b/cpp/src/arrow/flight/sql/odbc/odbc_api.cc
index e87e713caa88..23f7a2b011cf 100644
--- a/cpp/src/arrow/flight/sql/odbc/odbc_api.cc
+++ b/cpp/src/arrow/flight/sql/odbc/odbc_api.cc
@@ -179,12 +179,8 @@ SQLRETURN SQLFreeStmt(SQLHSTMT handle, SQLUSMALLINT option) {
     case SQL_CLOSE: {
       using ODBC::ODBCStatement;
 
-      ODBCStatement* statement = reinterpret_cast<ODBCStatement*>(handle);
-
-      return ODBCStatement::ExecuteWithDiagnostics(statement, SQL_ERROR, [=]() {
-        if (!statement) {
-          return SQL_INVALID_HANDLE;
-        }
+      return ODBCStatement::ExecuteWithDiagnostics(handle, SQL_ERROR, [=]() {
+        ODBCStatement* statement = reinterpret_cast<ODBCStatement*>(handle);
 
         // Close cursor with suppressErrors set to true
         statement->closeCursor(true);
@@ -1060,6 +1056,19 @@ SQLRETURN SQLBindCol(SQLHSTMT stmt, SQLUSMALLINT recordNumber, SQLSMALLINT cType
   });
 }
 
+SQLRETURN SQLCloseCursor(SQLHSTMT stmt) {
+  LOG_DEBUG("SQLCloseCursor called with stmt: {}", stmt);
+  using ODBC::ODBCStatement;
+  return ODBCStatement::ExecuteWithDiagnostics(stmt, SQL_ERROR, [=]() {
+    ODBCStatement* statement = reinterpret_cast<ODBCStatement*>(stmt);
+
+    // Close cursor with suppressErrors set to false
+    statement->closeCursor(false);
+
+    return SQL_SUCCESS;
+  });
+}
+
 SQLRETURN SQLGetData(SQLHSTMT stmt, SQLUSMALLINT recordNumber, SQLSMALLINT cType,
                      SQLPOINTER dataPtr, SQLLEN bufferLength, SQLLEN* indicatorPtr) {
   // GH-46979: support SQL_C_GUID data type
@@ -1080,7 +1089,6 @@ SQLRETURN SQLGetData(SQLHSTMT stmt, SQLUSMALLINT recordNumber, SQLSMALLINT cType
 
 SQLRETURN SQLMoreResults(SQLHSTMT stmt) {
   LOG_DEBUG("SQLMoreResults called with stmt: {}", stmt);
-  // TODO: write tests for SQLMoreResults
   using ODBC::ODBCStatement;
   // Multiple result sets not supported. Return SQL_NO_DATA by default.
   return ODBCStatement::ExecuteWithDiagnostics(stmt, SQL_ERROR, [=]() {
@@ -1092,7 +1100,6 @@ SQLRETURN SQLMoreResults(SQLHSTMT stmt) {
 SQLRETURN SQLNumResultCols(SQLHSTMT stmt, SQLSMALLINT* columnCountPtr) {
   LOG_DEBUG("SQLNumResultCols called with stmt: {}, columnCountPtr: {}", stmt,
             fmt::ptr(columnCountPtr));
-  // TODO: write tests for SQLNumResultCols
   using ODBC::ODBCStatement;
   return ODBCStatement::ExecuteWithDiagnostics(stmt, SQL_ERROR, [=]() {
     ODBCStatement* statement = reinterpret_cast<ODBCStatement*>(stmt);
@@ -1104,7 +1111,6 @@ SQLRETURN SQLNumResultCols(SQLHSTMT stmt, SQLSMALLINT* columnCountPtr) {
 SQLRETURN SQLRowCount(SQLHSTMT stmt, SQLLEN* rowCountPtr) {
   LOG_DEBUG("SQLRowCount called with stmt: {}, columnCountPtr: {}", stmt,
             fmt::ptr(rowCountPtr));
-  // TODO: write tests for SQLRowCount
   using ODBC::ODBCStatement;
   return ODBCStatement::ExecuteWithDiagnostics(stmt, SQL_ERROR, [=]() {
     ODBCStatement* statement = reinterpret_cast<ODBCStatement*>(stmt);
diff --git a/cpp/src/arrow/flight/sql/odbc/odbc_api.h b/cpp/src/arrow/flight/sql/odbc/odbc_api.h
index d9181ff329b6..e4139f963336 100644
--- a/cpp/src/arrow/flight/sql/odbc/odbc_api.h
+++ b/cpp/src/arrow/flight/sql/odbc/odbc_api.h
@@ -74,6 +74,7 @@ SQLRETURN SQLExtendedFetch(SQLHSTMT stmt, SQLUSMALLINT fetchOrientation,
 SQLRETURN SQLFetchScroll(SQLHSTMT stmt, SQLSMALLINT fetchOrientation, SQLLEN fetchOffset);
 SQLRETURN SQLBindCol(SQLHSTMT stmt, SQLUSMALLINT recordNumber, SQLSMALLINT cType,
                      SQLPOINTER dataPtr, SQLLEN bufferLength, SQLLEN* indicatorPtr);
+SQLRETURN SQLCloseCursor(SQLHSTMT stmt);
 SQLRETURN SQLGetData(SQLHSTMT stmt, SQLUSMALLINT recordNumber, SQLSMALLINT cType,
                      SQLPOINTER dataPtr, SQLLEN bufferLength, SQLLEN* indicatorPtr);
 SQLRETURN SQLMoreResults(SQLHSTMT stmt);
diff --git a/cpp/src/arrow/flight/sql/odbc/odbcabstraction/odbc_impl/odbc_statement.cc b/cpp/src/arrow/flight/sql/odbc/odbcabstraction/odbc_impl/odbc_statement.cc
index 70ee80ea08f2..c990f766df5f 100644
--- a/cpp/src/arrow/flight/sql/odbc/odbcabstraction/odbc_impl/odbc_statement.cc
+++ b/cpp/src/arrow/flight/sql/odbc/odbcabstraction/odbc_impl/odbc_statement.cc
@@ -703,7 +703,7 @@ void ODBCStatement::RevertAppDescriptor(bool isApd) {
 
 void ODBCStatement::closeCursor(bool suppressErrors) {
   if (!suppressErrors && !m_currenResult) {
-    throw DriverException("Invalid cursor state", "28000");
+    throw DriverException("Invalid cursor state", "24000");
   }
 
   if (m_currenResult) {
diff --git a/cpp/src/arrow/flight/sql/odbc/tests/statement_test.cc b/cpp/src/arrow/flight/sql/odbc/tests/statement_test.cc
index fee8ab5f7002..89fce1a23d22 100644
--- a/cpp/src/arrow/flight/sql/odbc/tests/statement_test.cc
+++ b/cpp/src/arrow/flight/sql/odbc/tests/statement_test.cc
@@ -2470,4 +2470,64 @@ TYPED_TEST(FlightSQLODBCTestBase, SQLNumResultColsFunctionSequenceErrorOnNoQuery
   this->disconnect();
 }
 
+TYPED_TEST(FlightSQLODBCTestBase, TestSQLFreeStmtSQLClose) {
+  this->connect();
+
+  std::wstring wsql = L"SELECT 1;";
+  std::vector<SQLWCHAR> sql0(wsql.begin(), wsql.end());
+
+  SQLRETURN ret =
+      SQLExecDirect(this->stmt, &sql0[0], static_cast<SQLINTEGER>(sql0.size()));
+
+  EXPECT_EQ(ret, SQL_SUCCESS);
+
+  ret = SQLFreeStmt(this->stmt, SQL_CLOSE);
+
+  EXPECT_EQ(ret, SQL_SUCCESS);
+
+  this->disconnect();
+}
+
+TYPED_TEST(FlightSQLODBCTestBase, TestSQLCloseCursor) {
+  this->connect();
+
+  std::wstring wsql = L"SELECT 1;";
+  std::vector<SQLWCHAR> sql0(wsql.begin(), wsql.end());
+
+  SQLRETURN ret =
+      SQLExecDirect(this->stmt, &sql0[0], static_cast<SQLINTEGER>(sql0.size()));
+
+  EXPECT_EQ(ret, SQL_SUCCESS);
+
+  ret = SQLCloseCursor(this->stmt);
+
+  EXPECT_EQ(ret, SQL_SUCCESS);
+
+  this->disconnect();
+}
+
+TYPED_TEST(FlightSQLODBCTestBase, TestSQLFreeStmtSQLCloseWithoutCursor) {
+  // SQLFreeStmt(SQL_CLOSE) does not throw error with invalid cursor
+  this->connect();
+
+  SQLRETURN ret = SQLFreeStmt(this->stmt, SQL_CLOSE);
+
+  EXPECT_EQ(ret, SQL_SUCCESS);
+
+  this->disconnect();
+}
+
+TYPED_TEST(FlightSQLODBCTestBase, TestSQLCloseCursorWithoutCursor) {
+  this->connect();
+
+  SQLRETURN ret = SQLCloseCursor(this->stmt);
+
+  EXPECT_EQ(ret, SQL_ERROR);
+
+  // Verify invalid cursor error state is returned
+  VerifyOdbcErrorState(SQL_HANDLE_STMT, this->stmt, error_state_24000);
+
+  this->disconnect();
+}
+
 }  // namespace arrow::flight::sql::odbc