The decision comes after an August 2018 crash involving a Ju-52 plane operated by Ju-Air in which 20 people died.
In a statement on Tuesday, FOCA said that commercial flights with historic planes no longer fulfilled current safety requirements.
But FOCA said that the three Ju-52 aircraft, which date back to the Second World War, could continue to be used by club members for private purposes as long as technical and operational flight requirements were met.
Passengers would also have to be fully informed of the risks.
The three Ju-52 planes operated by Ju-Air were grounded late last year in the wake of an interim report by the Swiss Transportation Safety Investigation Board (STSB) into the 2018 crash in the eastern canton of Graubünden.
The agency said there were significant cracks and corrosion to the main wing spar and other parts of the plane.
BAZL said this damage could not be uncovered during normal maintenance work and inspections.
But the agency also stressed it was not yet clear if that structural damage was responsible for the crash last year.
FOCA has demanded a range of safety revisions to the three Ju-52 aircraft which have not yet been fully implemented. It is not known when the aircraft will fly again.
Ju-Air said on Tuesday it was currently carrying out a complete restoration of its three remaining aircraft.
It plans to run a reduce service with one aircraft this summer.