It is unknown when it actually occurred. Glennon was evaluated for the concussion after the game, which he finished, spiking the ball before a field goal attempt on the Giants' final offensive play.
Glennon started in place of Daniel Jones, who was inactive because of a neck strain. Jones is not yet cleared for contact. It remains unknown if or when he will be able to return, even though he was on the field Sunday running through an extensive pregame workout.
Jones was believed to have hurt his neck on the second play in last week's win over the Philadelphia Eagles. He also finished that game.
Jones is expected to meet with doctors again on Monday morning.
"All of our players will have that day-after-game checkup with all the doctors," coach Joe Judge said. "Daniel will be no different than that. I'll check with the doctors [Monday] and continue with progression. They'll continue to evaluate him and when they deem he's ready to return to contact and play full, then we'll have them out there playing."
Jake Fromm, signed by the Giants off the Buffalo Bills' practice squad last week, is the only other quarterback on the team's active roster and could be in line to start next week against the Los Angeles Chargers if neither Glennon nor Jones are cleared for the game.
The Giants (4-8) also have former Michigan State quarterback Brian Lewerke on their practice squad.
Glennon completed 23-of-44 passes Sunday for 187 yards and threw an interception in the Giants' loss. He was sacked three times.
Glennon remained winless as a starter since 2017 when he was with the Chicago Bears. He would remain the starter if he's able to play and Jones didn't return.
"Yes," Judge said when asked about sticking with Glennon after Sunday's loss. "I would say at this point, yes."