Simply edit your theme functions.php file,
find :
register_sidebar function
check out the name attribute in the function to make sure which widget you are going to update
There should be an attribute called before_widget
you can define your custom CSS Class name into it
here is the sample code for your reference
register_sidebar( array(
'name' => __( 'News Sidebar', 'left-test-sidebar' ),
'id' => 'sidebar-1',
'description' => __( 'Add widgets here to appear in your sidebar.', 'depnet' ),
'before_widget' => '<section id="%1$s" class="widget %2$s YOUR-CUSTOM-CSS-CLASS">',
'after_widget' => '</section>',
'before_title' => '<div class="widget-title YOUR-CUSTOM-CSS-CLASS"><h4>',
'after_title' => '</h4></div>',
) );