Edit: if the field is an ACF field, then you can. Then you can use update_field like this update_field($selector, $value, $post_id);
You can save it like any other value except now you save an array.
$your_array = array( 'some value', 'other value' );
update_post_meta( $post_id, $meta_key, $your_array );
update_field( $meta_key, $your_array, $post_id );