diff --git a/x-pack/plugins/ml/public/application/components/data_grid/data_grid.tsx b/x-pack/plugins/ml/public/application/components/data_grid/data_grid.tsx
index 1949a3c339161..b36ee0fc32556 100644
--- a/x-pack/plugins/ml/public/application/components/data_grid/data_grid.tsx
+++ b/x-pack/plugins/ml/public/application/components/data_grid/data_grid.tsx
@@ -99,6 +99,14 @@ export const DataGrid: FC<Props> = memo(
     //   };
     // };
 
+    // If the charts are visible, hide the column actions icon.
+    const columnsWithChartsActionized = columnsWithCharts.map((d) => {
+      if (chartsVisible === true) {
+        d.actions = false;
+      }
+      return d;
+    });
+
     const popOverContent = useMemo(() => {
       return analysisType === ANALYSIS_CONFIG_TYPE.REGRESSION ||
         analysisType === ANALYSIS_CONFIG_TYPE.CLASSIFICATION
@@ -254,7 +262,7 @@ export const DataGrid: FC<Props> = memo(
         <div className="mlDataGrid">
           <EuiDataGrid
             aria-label={isWithHeader(props) ? props.title : ''}
-            columns={columnsWithCharts.map((c) => {
+            columns={columnsWithChartsActionized.map((c) => {
               c.initialWidth = 165;
               return c;
             })}