Is it permissible to pay Zakat from funds invested for the benefit of the mosque?

If the funds are endowed (waqf) for the mosque, there is no zakat due on them. However, if they are owned by a specific individual who donates their proceeds to the mosque, then zakat is obligatory on them, provided the conditions for its obligation are met, namely reaching the nisab (minimum threshold) and the passing of a hawl (one lunar year).