diff --git a/packages/edit-site/src/components/global-styles/font-library-modal/index.js b/packages/edit-site/src/components/global-styles/font-library-modal/index.js
index dc0fcd7ea373b0..481befaf6e3c0f 100644
--- a/packages/edit-site/src/components/global-styles/font-library-modal/index.js
+++ b/packages/edit-site/src/components/global-styles/font-library-modal/index.js
@@ -6,6 +6,8 @@ import {
 	Modal,
 	privateApis as componentsPrivateApis,
 } from '@wordpress/components';
+import { store as coreStore } from '@wordpress/core-data';
+import { useSelect } from '@wordpress/data';
 import { useContext } from '@wordpress/element';
 
 /**
@@ -19,16 +21,15 @@ import { unlock } from '../../../lock-unlock';
 
 const { Tabs } = unlock( componentsPrivateApis );
 
-const DEFAULT_TABS = [
-	{
-		id: 'installed-fonts',
-		title: __( 'Library' ),
-	},
-	{
-		id: 'upload-fonts',
-		title: __( 'Upload' ),
-	},
-];
+const DEFAULT_TAB = {
+	id: 'installed-fonts',
+	title: __( 'Library' ),
+};
+
+const UPLOAD_TAB = {
+	id: 'upload-fonts',
+	title: __( 'Upload' ),
+};
 
 const tabsFromCollections = ( collections ) =>
 	collections.map( ( { slug, name } ) => ( {
@@ -44,11 +45,17 @@ function FontLibraryModal( {
 	defaultTabId = 'installed-fonts',
 } ) {
 	const { collections, setNotice } = useContext( FontLibraryContext );
+	const canUserCreate = useSelect( ( select ) => {
+		const { canUser } = select( coreStore );
+		return canUser( 'create', 'font-families' );
+	}, [] );
+
+	const tabs = [ DEFAULT_TAB ];
 
-	const tabs = [
-		...DEFAULT_TABS,
-		...tabsFromCollections( collections || [] ),
-	];
+	if ( canUserCreate ) {
+		tabs.push( UPLOAD_TAB );
+		tabs.push( ...tabsFromCollections( collections || [] ) );
+	}
 
 	// Reset notice when new tab is selected.
 	const onSelect = () => {
diff --git a/packages/edit-site/src/components/global-styles/font-library-modal/installed-fonts.js b/packages/edit-site/src/components/global-styles/font-library-modal/installed-fonts.js
index 9425cb9c2d27ba..226e9cf5a3eefc 100644
--- a/packages/edit-site/src/components/global-styles/font-library-modal/installed-fonts.js
+++ b/packages/edit-site/src/components/global-styles/font-library-modal/installed-fonts.js
@@ -18,6 +18,8 @@ import {
 	Spinner,
 	privateApis as componentsPrivateApis,
 } from '@wordpress/components';
+import { store as coreStore } from '@wordpress/core-data';
+import { useSelect } from '@wordpress/data';
 import { useContext, useEffect, useState } from '@wordpress/element';
 import { __, sprintf } from '@wordpress/i18n';
 import { chevronLeft } from '@wordpress/icons';
@@ -49,9 +51,24 @@ function InstalledFonts() {
 		setNotice,
 	} = useContext( FontLibraryContext );
 	const [ isConfirmDeleteOpen, setIsConfirmDeleteOpen ] = useState( false );
+	const customFontFamilyId =
+		libraryFontSelected?.source === 'custom' && libraryFontSelected?.id;
+
+	const canUserDelete = useSelect(
+		( select ) => {
+			const { canUser } = select( coreStore );
+			return (
+				customFontFamilyId &&
+				canUser( 'delete', 'font-families', customFontFamilyId )
+			);
+		},
+		[ customFontFamilyId ]
+	);
 
 	const shouldDisplayDeleteButton =
-		!! libraryFontSelected && libraryFontSelected?.source !== 'theme';
+		!! libraryFontSelected &&
+		libraryFontSelected?.source !== 'theme' &&
+		canUserDelete;
 
 	const handleUninstallClick = () => {
 		setIsConfirmDeleteOpen( true );