Boss Frank Lampard confirmed the England hitman will miss Saturday's FA Cup trip to Hull, but conceded the Blues are still waiting to find out how long he will be sidelined.
Abraham limped off the field at full-time after Chelsea's 2-2 Premier League draw with Arsenal at Stamford Bridge on Tuesday night.
"The good news is he hasn't fractured anything, but the other news is we still have to see how he develops," said Lampard.
"He's not fit for the weekend, but whether he'll be fit for Leicester I'm still not sure. It's still not clear at the moment."
Chelsea face a challenging Premier League trip to Leicester on Saturday, February 1. The Blues also face Manchester United and Tottenham in a pivotal schedule in February, with Lampard keen to see his 13-goal Premier League striker back to fitness as quickly as possible.
Lampard last week refused to dampen down links to wantaway PSG striker Edinson Cavani, and continues to admit the Blues are keen to recruit a forward this month.
And the Chelsea boss said Abraham's injury is "very relevant" to the club's striker search.
"I think the impetus to bring in a striker or players potentially that can get on the end of these chances we're creating is there, we have to be honest," said Lampard.
"When you're creating 20 chances a game and not scoring enough goals that can be crucial. I don't think it absolutely changes it but Tammy has been our main source of goals, so yes, it's very relevant.
"I think there's choice (in the transfer market), but it's not the ideal window, history's proven that.
"I think it's about trying to get the choice right of the player we can bring in considering what's available.
"The club know, and the games are showing that, my thoughts on that. So we'll have to see how that goes between now and the end of the window."