Jota, 25, was taken off on a stretcher deep into stoppage time during Liverpool's 1-0 Premier League win against champions Manchester City at the weekend.
"Really not good news about Diego. I guess he will miss the World Cup," Klopp said. "Pretty serious injury in the muscle, calf muscle, and now we have to recover. He starts all, the process starts let me say. That's it pretty much, that's the first diagnosis that's pretty clear and all the rest will now follow in the next few days. Very sad news for the boy, for us of course as well, for Portugal for everybody."
Jota, capped 29 times by Portugal, has scored 10 times for the national team.
Klopp also said he expected to be on the touchline against West Ham United in the Premier League at Anfield on Wednesday, despite being shown a red card in the feisty win over Liverpool on Sunday.
"I think I will be there tomorrow because nothing really happened yet. I don't think something will happen tomorrow to be honest, a few hours before the game."