The 19-year-old driver is appearing at Donington Park for the first time since his crash in April 2017.
Monger grabbed pole ahead of Carlin team-mate Nicolai Kjaergaard by 0.173 seconds.
"All the dry testing we have done beforehand, the car has felt really good and we've just been quick from the start," said Monger.
Floersch released from hospital after horror crash
"Donington Park is one of my favourite circuits and although it's weird coming back here with what happened I've always enjoyed the circuit.
"I did two laps that were good enough for pole and I have to thank everyone from Carlin for the car. We're quick in the wet or dry and I'm starting in the best place possible.
"The start is going to be important as following people around here can be difficult."
F3 driver Floersch vows to return after horror crash