Source:
Fatāwā Muḥammadiyyah, Vol. 1, Page 570
Question:
If a free dispensary is established using Zakat funds, is it also permissible to pay the salaries of the dispensary staff and doctors from the same Zakat money?
Answer:
Al-ḥamdu lillāh, waṣ-ṣalātu was-salāmu ʿalā Rasūlillāh, ammā baʿd!
When the use of Zakat funds for establishing a free dispensary is deemed permissible, then it is likewise permissible to pay the salaries of its staff members and doctors from those same Zakat funds.
هٰذَا مَا عِندِي وَاللّٰهُ أَعْلَمُ بِالصَّوَابِ
This is what I hold to be correct, and Allah knows best what is right.