diff --git a/includes/class-wc-install.php b/includes/class-wc-install.php
index 713407e1509..725fe1d47eb 100644
--- a/includes/class-wc-install.php
+++ b/includes/class-wc-install.php
@@ -597,19 +597,18 @@ class WC_Install {
 
 		// Add constraint to download logs if the columns matches.
 		if ( ! empty( $download_permissions_column_type ) && ! empty( $download_log_column_type ) && $download_permissions_column_type === $download_log_column_type ) {
-			$constraint_prefix = ! is_multisite() || ( is_main_site() && is_main_network() ) ? 'fk_' . $wpdb->prefix : str_replace( $wpdb->base_prefix, 'fk_', $wpdb->prefix );
 			$fk_result = $wpdb->get_row( "
 				SELECT COUNT(*) AS fk_count
 				FROM information_schema.TABLE_CONSTRAINTS
 				WHERE CONSTRAINT_SCHEMA = '{$wpdb->dbname}'
-				AND CONSTRAINT_NAME = '{$constraint_prefix}wc_download_log_permission_id'
+				AND CONSTRAINT_NAME = 'fk_{$wpdb->prefix}wc_download_log_permission_id'
 				AND CONSTRAINT_TYPE = 'FOREIGN KEY'
 				AND TABLE_NAME = '{$wpdb->prefix}wc_download_log'
 			" ); // WPCS: unprepared SQL ok.
 			if ( 0 === (int) $fk_result->fk_count ) {
 				$wpdb->query( "
 					ALTER TABLE `{$wpdb->prefix}wc_download_log`
-					ADD CONSTRAINT `{$constraint_prefix}wc_download_log_permission_id`
+					ADD CONSTRAINT `fk_{$wpdb->prefix}wc_download_log_permission_id`
 					FOREIGN KEY (`permission_id`)
 					REFERENCES `{$wpdb->prefix}woocommerce_downloadable_product_permissions` (`permission_id`) ON DELETE CASCADE;
 				" ); // WPCS: unprepared SQL ok.