The Nottingham Forest midfield suffered the problem in training on Saturday morning, having come on as a substitute during the previous night's 3-0 win over Latvia.
Reid was among a series of players being assessed, with West Ham defender Joey O'Brien due to have a scan on a hamstring problem and Sean St Ledger also a doubt for Tuesday night's trip to Poland.
O'Brien was not risked for the match by Ireland boss Martin O'Neill, and the player also sat out training in Malahide on Saturday.
O'Neill admitted he does not know the extent of the damage, but he is hopeful the 27-year-old will return to action swiftly.
"He's going for a scan. We are not sure," O'Neill said. "He just felt a little bit last night in the warm-up.
"So even though there was an opportunity last night to play him, we wouldn't have done so just because there might be some risk, so he is going for a scan later on.
"It's his hamstring. He just felt a little bit sore and it is just precautionary. But he wasn't too bad."