The midfielder has missed the club's last four games after damaging his ankle ligaments during a 1-0 defeat to Arsenal at the end of February.
Tielemans was reportedly making good progress in his rehabilitation, but inflammation is set to delay his recovery by a few weeks.
"Sadly, he's had a slight setback," Rodgers told reporters ahead of Saturday's Premier League meeting with Crystal Palace.
"He was due to train this week. He was training really well right until last Friday, but then had a slight setback that might mean he needs a rest for a few extra weeks.
"It's disappointing for us, but we have to let the ankle settle back down and then take it from there."
The Leicester boss was then asked whether Tielemans would only be available for a "handful" of games this season.
"Yeah, that's probably about right," Rodgers replied. "It's a shame because he'd been doing so well. But he's got this irritation."
News of the midfielder's injury setback will certainly come as a blow, especially as Tielemans appears to be coming to the end of his Leicester career.
The Belgium international is out of contract in June, and he is widely expected to leave the club on a free transfer.
Like Tielemans, Jonny Evans is expected to miss Saturday's Premier League encounter, but the Northern Ireland international is closing in on a return after participating in training this week.
Rodgers expects defenders Victor Kristiansen and Harry Souttar will overcome their fitness issues to feature on Saturday.
The Leicester manager is also hopeful that Dennis Praet will be available, despite sustaining a dead leg on international duty with Belgium.
The Foxes head into the weekend in 17th place in the Premier League table with just one point separating them from the drop zone.