Martin was competing at his first Grand Prix weekend after missing the opening three rounds following a nasty crash in pre-season testing where he fractured his foot and hand, which required surgery.
The Spaniard went down at the kerb on turn 11 under the lights at the Lusail International Circuit and he was struggling to get back on his feet before being taken to the medical centre.
"Jorge Martin underwent a CT scan that showed an increase in the pneumothorax, this will make it necessary to place a drainage in aspiration," Aprilia said in a statement.
"The rider will have to remain under observation for a few days in the hospital until the pneumothorax resolves."
Aprilia did not give a potential timeline on his return, with the next round in two weeks' time on home turf at the Spanish Grand Prix.
Ducati's Marc Marquez won the race in Qatar to extend his lead over his younger brother Alex in the rider's championship to 18 points.