diff --git a/CHANGELOG.md b/CHANGELOG.md
index c396cdbe5..181b4ccc4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,7 @@ This project adheres to [Semantic Versioning](http://semver.org/).
 ## [Unreleased]
 ### Fixed
 - [#722](https://github.com/plotly/dash-table/pull/722) Fix a bug where row height is misaligned when using fixed_columns and/or fixed_rows
+- [#728](https://github.com/plotly/dash-table/pull/728) Fix copy/paste on readonly cells
 
 ## [4.6.2] - 2020-04-01
 ### Changed
diff --git a/src/dash-table/components/CellLabel/index.tsx b/src/dash-table/components/CellLabel/index.tsx
index 03ff5f96b..7a0d2b7e1 100644
--- a/src/dash-table/components/CellLabel/index.tsx
+++ b/src/dash-table/components/CellLabel/index.tsx
@@ -44,6 +44,7 @@ export default class CellLabel extends PureComponent<IProps> {
         const el = this.refs.el as HTMLDivElement;
 
         if (applyFocus && el && document.activeElement !== el) {
+            window.getSelection()?.selectAllChildren(el);
             el.focus();
         }
     }
diff --git a/src/dash-table/components/Table/Table.less b/src/dash-table/components/Table/Table.less
index 596976ad1..7162d7034 100644
--- a/src/dash-table/components/Table/Table.less
+++ b/src/dash-table/components/Table/Table.less
@@ -396,20 +396,22 @@
                 .dash-cell-value {
                     height: 100%;
                     width: 100%;
-                }
 
-                input.dash-cell-value {
-                    position: absolute;
-                    left: 0;
-                    top: 0;
                     &.unfocused::selection {
                         background-color: transparent;
                     }
+
                     &.unfocused {
                         caret-color: transparent;
                     }
                 }
 
+                input.dash-cell-value {
+                    position: absolute;
+                    left: 0;
+                    top: 0;
+                }
+
                 .cell-value-shadow {
                     margin: auto 0;
                     opacity: 0;