James, named as Chelsea captain during the summer, left the pitch in the second half of their 1-1 draw with Liverpool on Saturday. The manager said he was suffering from fatigue but the defender has now picked up a muscle injury.
"It's a hamstring. It's not a few days, a few weeks maybe," Pochettino told reporters.
"I think it's a sad moment because he's our captain, he was so excited to be the captain, full of energy. We are going to assess him day by day," the manager added.
Chelsea signed Moises Caicedo and Romeo Lavia this week, and the Argentine spoke highly of both players.
"To add this kind of player, it's fantastic work from the club. It shows the work the owners and sporting directors are doing," Pochettino said about Caicedo who arrived for a reported British record fee of £115 million ($146 million).
Lavia signed from Southampton on Friday and Pochettino is looking forward to having him at the club.
"I think we all know him, his quality, his profile. He's the perfect player for this project. We are excited and happy to add him in the squad."
The new arrivals may need to wait before making their Chelsea debuts.
"We need to assess them. They have been stressful weeks for Moises and Romeo. We don't need to rush them. If they are ready tomorrow (Saturday) they will be involved. If not, we will wait a few days more."
Liverpool had been strongly linked with both players, but in the end, it was Chelsea who won the race for their signatures.
"That is the players' decision. They decide to come here. I think it's not a competition. It makes us happy and they talk very highly about our owners," the manager said.
Chelsea travel to London Stadium on Saturday to face a West Ham side who also drew their opening game in a 1-1 draw at Bournemouth last weekend.
