diff --git a/changelog/fix-7960-transaction-refund-eligible-disputes-only b/changelog/fix-7960-transaction-refund-eligible-disputes-only
new file mode 100644
index 00000000000..e35c11107f7
--- /dev/null
+++ b/changelog/fix-7960-transaction-refund-eligible-disputes-only
@@ -0,0 +1,4 @@
+Significance: patch
+Type: fix
+
+Hide the transaction details refund menu for ineligble disputed transactions
diff --git a/client/disputes/utils.ts b/client/disputes/utils.ts
index 6e5acf2f437..d4cb2fc52d1 100644
--- a/client/disputes/utils.ts
+++ b/client/disputes/utils.ts
@@ -72,6 +72,11 @@ export const isInquiry = ( dispute: Pick< Dispute, 'status' > ): boolean => {
 	return dispute.status.startsWith( 'warning' );
 };
 
+export const isRefundable = ( status: DisputeStatus ): boolean => {
+	// Refundable dispute statuses are one of `warning_needs_response`, `warning_under_review`, `warning_closed` or `won`.
+	return isInquiry( { status } ) || 'won' === status;
+};
+
 /**
  * Returns the dispute fee balance transaction for a dispute if it exists
  * and the deduction has not been reversed.
diff --git a/client/payment-details/summary/index.tsx b/client/payment-details/summary/index.tsx
index 607bacb5f0a..58db34e8da3 100644
--- a/client/payment-details/summary/index.tsx
+++ b/client/payment-details/summary/index.tsx
@@ -48,6 +48,7 @@ import DisputeStatusChip from 'components/dispute-status-chip';
 import {
 	getDisputeFeeFormatted,
 	isAwaitingResponse,
+	isRefundable,
 } from 'wcpay/disputes/utils';
 import { useAuthorization } from 'wcpay/data';
 import CaptureAuthorizationButton from 'wcpay/components/capture-authorization-button';
@@ -208,6 +209,15 @@ const PaymentDetailsSummary: React.FC< PaymentDetailsSummaryProps > = ( {
 	const disputeFee =
 		charge.dispute && getDisputeFeeFormatted( charge.dispute );
 
+	// If this transaction is disputed, check if it is refundable.
+	const isDisputeRefundable = charge.dispute
+		? isRefundable( charge.dispute.status )
+		: true;
+
+	// Control menu only shows refund actions for now. In the future, it may show other actions.
+	const showControlMenu =
+		charge.captured && ! charge.refunded && isDisputeRefundable;
+
 	// Use the balance_transaction fee if available. If not (e.g. authorized but not captured), use the application_fee_amount.
 	const transactionFee = charge.balance_transaction
 		? {
@@ -484,7 +494,7 @@ const PaymentDetailsSummary: React.FC< PaymentDetailsSummaryProps > = ( {
 						</div>
 					</div>
 					<div className="payment-details__refund-controls">
-						{ ! charge?.refunded && charge?.captured && (
+						{ showControlMenu && (
 							<Loadable
 								isLoading={ isLoading }
 								placeholder={ moreVertical }
diff --git a/client/payment-details/summary/test/index.test.tsx b/client/payment-details/summary/test/index.test.tsx
index 522c613d5ff..8f41921aae5 100755
--- a/client/payment-details/summary/test/index.test.tsx
+++ b/client/payment-details/summary/test/index.test.tsx
@@ -427,6 +427,13 @@ describe( 'PaymentDetailsSummary', () => {
 		screen.getByRole( 'button', {
 			name: /Accept dispute/,
 		} );
+
+		// Refund menu is not rendered
+		expect(
+			screen.queryByRole( 'button', {
+				name: /Translation actions/i,
+			} )
+		).toBeNull();
 	} );
 
 	test( 'renders the information of a disputed charge when the store/charge currency differ', () => {
@@ -684,6 +691,11 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is rendered
+		screen.getByRole( 'button', {
+			name: /Translation actions/i,
+		} );
 	} );
 
 	test( 'correctly renders dispute details for "under_review" disputes', () => {
@@ -712,6 +724,13 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is not rendered
+		expect(
+			screen.queryByRole( 'button', {
+				name: /Translation actions/i,
+			} )
+		).toBeNull();
 	} );
 
 	test( 'correctly renders dispute details for "accepted" disputes', () => {
@@ -744,6 +763,13 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is not rendered
+		expect(
+			screen.queryByRole( 'button', {
+				name: /Translation actions/i,
+			} )
+		).toBeNull();
 	} );
 
 	test( 'correctly renders dispute details for "lost" disputes', () => {
@@ -777,6 +803,13 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is not rendered
+		expect(
+			screen.queryByRole( 'button', {
+				name: /Translation actions/i,
+			} )
+		).toBeNull();
 	} );
 
 	test( 'correctly renders dispute details for "warning_needs_response" inquiry disputes', () => {
@@ -807,6 +840,11 @@ describe( 'PaymentDetailsSummary', () => {
 		screen.getByRole( 'button', {
 			name: /Issue refund/i,
 		} );
+
+		// Refund menu is rendered
+		screen.getByRole( 'button', {
+			name: /Translation actions/i,
+		} );
 	} );
 
 	test( 'correctly renders dispute details for "warning_under_review" inquiry disputes', () => {
@@ -834,6 +872,11 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is rendered
+		screen.getByRole( 'button', {
+			name: /Translation actions/i,
+		} );
 	} );
 
 	test( 'correctly renders dispute details for "warning_closed" inquiry disputes', () => {
@@ -862,6 +905,11 @@ describe( 'PaymentDetailsSummary', () => {
 				name: /Accept/i,
 			} )
 		).toBeNull();
+
+		// Refund menu is rendered
+		screen.getByRole( 'button', {
+			name: /Translation actions/i,
+		} );
 	} );
 
 	describe( 'order missing notice', () => {