The Gers forward came off during the second-half of the 2-0 defeat to Lyon in their Europa League Group opener at Ibrox on Thursday night.
Gerrard also revealed striker Alfredo Morelos is a doubt for the cinch Premiership clash with Motherwell at Ibrox on Sunday.
The Light Blues manger said: "We certainly have a problem with Ryan Kent, he will be sent for a scan probably late afternoon or early evening but he is obviously going to be out for the weekend.
"If the doctor's prediction is right he could miss a few weeks but we will know more this evening.
"Ryan had a rest in the international break, he trained well during the week. I don't think he has been carrying any problem that got worse, this is just an isolated incident.
"You could see clearly that he pulled up with something, hopefully it is not as bad as it looked.
"The good thing is, if it is a hamstring injury, that might be three to four weeks which they normally are, we have an international break in that period to try and get him ready but I think he will definitely be missing for a few weeks if the doctor's prediction is right.
"We also have Alfredo Morelos with a bit of a tight hamstring, not on Ryan Kent's level but we might send him for a picture as well just to be sure on that one. So Alfredo is a doubt as well."
Gerrard knows he has no time to dwell on Thursday's European disappointment as they look to retain top spot in the league on the day that the 55th cinch Premiership flag is unfurled.
He said: "We put a big effort into last night's game with no reward.
"So it is a case of picking the boys up and getting them recovered because the Motherwell game comes on us pretty quickly.
"We will see who is available, train the boys who weren't involved and then tomorrow we will go tactically into the Motherwell game.
"So it happens pretty quick, the games come thick and fast, I think it is three games in six days so we have no time to dwell, we have to move on pretty fast."
Gerrard believes that due to Covid-19 issues and injuries, squad depth will be even more vital this season.
He said: "You have to almost wait until the last minute before you can confirm a team.
"We are still testing a couple of times a week and with the injuries we have got at the moment it is very difficult to find that rhythm and settled team that I am looking for.
"So I think the squad, even more so than the previous three years, is going to be more important come the end of the season because it seems like the team is going to be changing an awful lot more and that is not going to be down to just rotation, it is going to be down to Covid and injury issues as well."