The Scottish champions' attacking burden was on Griffiths' shoulders in Dembele's absence but he suffered a calf problem in Scotland's 2-0 victory over Malta on Tuesday night.
Rodgers bolstered his attacking forces before the end of the transfer window with the signings of Manchester City winger Patrick Roberts and PSG young prospect Odsonne Edouard, both on a season-long loan.
Both new signings took part in training on Thursday, along with Dembele who has returned from injury, but according to Rodgers, only Edouard has a chance of being involved against Hamilton after the 19-year-old has adapted quickly to his new environment
Rodgers said: "I don't think Leigh can play tomorrow (Friday), it's as simple as that.
"He came off (on Monday) and he had a scan on his calf. We think he will be fine for Tuesday but yes, there is too much risk.
"Leigh took a knock on his calf and he has had these issues with his calves but we are hopeful this is not going to be that long and the Astroturf pitch at Hamilton is not ideal for him.
"There is a chance (Edouard could start).
"He is in the squad. He is very quick, very dynamic, technically very strong, of course he is still adapting.
"I don't think he has ever trained at 11 o'clock in the morning in the rain and with the floodlights on. He looked a bit cold this morning. He will be adapting to Scottish football."
The Northern Irish boss is urging caution on Dembele's return, as the French striker has only played in the two Champions League qualifiers against Linfield this season after damaging his hamstring.
He said: "He went to Clairefontaine in France for three weeks and did some great work with the medical team there, like he did here before he left.
"He is now back and we will assess him to see where he is at. The most important thing is that we can't risk it.
"Of course everyone would love to be involved in the Paris game but if not then he is not going to be too far away from that and then he is still going to have an impact for the remainder of the Champions League campaign, which is great news.
"But we have to be sure that he is right if he has any involvement in the game on Tuesday."