James was forced off in the first half of the 2-0 defeat at Goodison Park.
The right-back, who has only recently returned from a hamstring injury, looked dejected as he had to be replaced after just 27 minutes.
Chelsea also lost goalkeeper Robert Sanchez and left-back Marc Cucurella to injuries on Merseyside.
Speaking after another disappointing defeat left Chelsea in the bottom half of the Premier League table, Pochettino said: "He feels something in his hamstring; we don’t know the nature."
“Robert Sanchez suffered a problem against Manchester United, was an issue in his knee and felt something in his second half, that is why he asked for the change. Marc Cucurella twisted his ankle; big issues are happening and I hope he can recover as soon as possible.
"From the beginning, we are dealing with this kind of situation."
James was making just his fifth Premier League start of the season.
He did not receive any treatment on the pitch but had to be replaced by Levi Colwill on Merseyside.
Chelsea were without James for more than two months after he injured his hamstring against Liverpool on the opening day of the season.
His fitness issues are becoming a major concern for the Blues.