A TRACON Controller reported they released an IFR Departure at a non towered airport from a runway the departure procedure was not authorized for due to obstructions.

Narrative

Prior to ZZZ Tower opening; Aircraft X called on my approach control freq.; XXX.X; to collect his IFR clearance which I provided. Shortly there after the Pilot called looking for his IFR release and stated he was coming off Runway XX. I called ZZZ1 Tower to make them aware of the traffic; due to the close proximity of the airports and released Aircraft X on a 270 degree heading due to traffic departing ZZZ1 Runway XY on a 340 degree hdg. Shortly there after ZZZ1 Tower called to verify what runway Aircraft X was coming off of and reminded me that IFR departure off Runway XX was NA due to obstructions. I called Aircraft X to see if he was rolling and the pilot said he was so it was too late to stop him. I didn't state 'released Runway XX' since; at that point; it was a non tower controlled airport.The restriction is noted but you have to find it under the ZZZ tab by selecting the AFD tab. This is something that just has to be known and readily recallable when this happens; which is rarely.