diff --git a/src/wp-admin/includes/class-plugin-upgrader.php b/src/wp-admin/includes/class-plugin-upgrader.php
index c5476c886b..53c7da1ced 100644
--- a/src/wp-admin/includes/class-plugin-upgrader.php
+++ b/src/wp-admin/includes/class-plugin-upgrader.php
@@ -441,6 +441,31 @@ class Plugin_Upgrader extends WP_Upgrader {
 			return new WP_Error( 'incompatible_archive_no_plugins', $this->strings['incompatible_archive'], __( 'No valid plugins were found.' ) );
 		}
 
+		$requires_php = isset( $info['RequiresPHP'] ) ? $info['RequiresPHP'] : null;
+		$requires_wp  = isset( $info['RequiresWP'] ) ? $info['RequiresWP'] : null;
+
+		if ( ! is_php_version_compatible( $requires_php ) ) {
+			$error = sprintf(
+				/* translators: 1: Current PHP version, 2: Version required by the uploaded plugin. */
+				__( 'The PHP version on your server is %1$s, however the uploaded plugin requires %2$s.' ),
+				phpversion(),
+				$requires_php
+			);
+
+			return new WP_Error( 'incompatible_php_required_version', $this->strings['incompatible_archive'], $error );
+		}
+
+		if ( ! is_wp_version_compatible( $requires_wp ) ) {
+			$error = sprintf(
+				/* translators: 1: Current WordPress version, 2: Version required by the uploaded plugin. */
+				__( 'Your WordPress version is %1$s, however the uploaded plugin requires %2$s.' ),
+				$GLOBALS['wp_version'],
+				$requires_wp
+			);
+
+			return new WP_Error( 'incompatible_wp_required_version', $this->strings['incompatible_archive'], $error );
+		}
+
 		return $source;
 	}
 
diff --git a/src/wp-admin/includes/class-theme-installer-skin.php b/src/wp-admin/includes/class-theme-installer-skin.php
index 76d2030f6d..cd6145a978 100644
--- a/src/wp-admin/includes/class-theme-installer-skin.php
+++ b/src/wp-admin/includes/class-theme-installer-skin.php
@@ -221,7 +221,7 @@ class Theme_Installer_Skin extends WP_Upgrader_Skin {
 
 		echo '<h2 class="update-from-upload-heading">' . esc_html( __( 'This theme is already installed.' ) ) . '</h2>';
 
-		// Check errors for current theme
+		// Check errors for current theme.
 		if ( is_wp_error( $current_theme_data->errors() ) ) {
 			$this->feedback( 'current_theme_has_errors', $current_theme_data->errors()->get_error_message() );
 		}
diff --git a/src/wp-admin/includes/class-theme-upgrader.php b/src/wp-admin/includes/class-theme-upgrader.php
index 4ff5109e63..a5901b9fc7 100644
--- a/src/wp-admin/includes/class-theme-upgrader.php
+++ b/src/wp-admin/includes/class-theme-upgrader.php
@@ -588,7 +588,32 @@ class Theme_Upgrader extends WP_Upgrader {
 			);
 		}
 
+		$requires_php = isset( $info['RequiresPHP'] ) ? $info['RequiresPHP'] : null;
+		$requires_wp  = isset( $info['RequiresWP'] ) ? $info['RequiresWP'] : null;
+
+		if ( ! is_php_version_compatible( $requires_php ) ) {
+			$error = sprintf(
+				/* translators: 1: Current PHP version, 2: Version required by the uploaded theme. */
+				__( 'The PHP version on your server is %1$s, however the uploaded theme requires %2$s.' ),
+				phpversion(),
+				$requires_php
+			);
+
+			return new WP_Error( 'incompatible_php_required_version', $this->strings['incompatible_archive'], $error );
+		}
+		if ( ! is_wp_version_compatible( $requires_wp ) ) {
+			$error = sprintf(
+				/* translators: 1: Current WordPress version, 2: Version required by the uploaded theme. */
+				__( 'Your WordPress version is %1$s, however the uploaded theme requires %2$s.' ),
+				$GLOBALS['wp_version'],
+				$requires_wp
+			);
+
+			return new WP_Error( 'incompatible_wp_required_version', $this->strings['incompatible_archive'], $error );
+		}
+
 		$this->new_theme_data = $info;
+
 		return $source;
 	}