The 21-year-old picked up the injury on international duty with Israel and subsequently missed their two Euro 2024 qualifiers against Romania and Belarus.
Abada has featured in each of Celtic's opening four Scottish Premiership fixtures this term, chipping in with one goal and one assist, but Rodgers will now have to cope without the youngster for some time.
"He has gone to London today for a scan, but we think it is going to be around three to four months," Rodgers told reporters as quoted by BBC Sport.
"It looks like he has done his thigh muscle. He picked it up at the end of training in a shooting exercise.
"It is a real shame for him because he has done well over pre-season and he has started in a lot of games since I have been here, so we are really disappointed, but it is a squad game for us and we have other players to come in."
Rodgers has admitted that he was "looking forward" to working with Abada, who recently put pen to paper on a new four-year contract at Parkhead until the summer of 2027.
"He signed a new deal and he seemed happy and I was looking forward to continuing his development because he has lots of areas that he can improve on," Rodgers added.
"It is a shame but he will work hard and get back and we will use him for the second part of the season."
Rodgers has also confirmed that new signing Luis Palma is doubtful for Saturday's Premiership clash with Dundee as the Honduran winger is scheduled to return to Scotland on Friday.
Cameron Carter-Vickers, Marco Tilio, Maik Nawrocki, James McCarthy and Stephen Welsh all remain in the treatment room, although the former is hoping to return to action next month, while Reo Hatate and Yuki Kobayashi have recovered from injury and are available for selection on Saturday.
"Luis Palma won't be back until tomorrow (Friday), so we have to have a wee look at that, it's a long way he's travelled," said the Northern Irishman.
"Reo Hatate will be back which is great news for us. [Yuki] Kobayashi is back now training as well. Marco Tilio's been back now training but he missed pre-season so we're just waiting for the right moment again for him.
"Cameron Carter-Vickers is doing very well, hopefully on schedule to be back beginning of October, Maik Nawrocki obviously a bit longer."
While Palma may have to wait a little longer to make his Celtic debut, fellow new recruits Nat Phillips and Paulo Bernardo have both trained with their new teammates and are in contention to play at Parkhead on Saturday.
Celtic currently sit joint-top of the Premiership table with Motherwell on 10 points after four matches, and they will be looking to extend their unbeaten league run with success over Dundee.