The west London club, who have won just once in the Premier League so far this season, secured a much-needed victory in the Carabao Cup, but the result came at a cost when Chilwell was forced off with a hamstring injury in second-half stoppage time.
"I think it is bad news, what the doctor told me is not a good thing. It looks a bad injury so we will assess in the next days and we will see the period he is going to be absent from the squad," Pochettino said in a news conference ahead of Chelsea's Premier League match against Fulham on Monday.
"We are really sad about the news about Ben. The time[scale] is difficult to say now. The doctor will tell us and the club will communicate."
Pochettino said he is more optimistic regarding some of the team's other injury concerns.
Midfielder Carney Chukwuemeka has not played since Aug. 20 with a knee injury, but returned to training this week.
"I hope that maybe Carney, and of course Noni [Madueke] also, after his issue when he came back from the national team, he's getting ready.
"I hope that these two players will maybe be available for selection on Monday."
Chelsea have scored just five goals in the Premier League so far this season and have failed to score in their last three league games.
Nicolas Jackson scored the only goal of Wednesday's Carabao Cup victory, but the forward, who also scored Chelsea's last league goal back in August, is unavailable for the trip to Fulham because of suspension.
Pochettino said he is is still deciding on how best to set up his team to cope with Jackson's absence.
"We have a few options, to play with a striker and without a striker. We need to assess the whole squad after the game, things appear after 48 hours and we need to see how they are and how they recover from Wednesday," he said.
"The most important thing is to adapt, the squad needs to find a way to perform, that is the most important."
Chelsea are in 14th place in the table with five points, with Fulham three points ahead in 11th.