The winger was stretchered off in the closing stages of Liverpool's 1-0 Premier League win over Manchester City on Sunday.
"Not good news about Diogo -- yes he will miss the World Cup," Klopp said at a press conference ahead of Wednesday's home match against West Ham.
"(It's a) pretty serious injury in the calf muscle and now the recovery process starts. That's it pretty much.
"That is the first diagnosis, which was pretty clear, and all the rest will now follow in the next few days. It is very sad news for the boy, and for us as well of course and for Portugal."
Klopp, who said Jota would not need an operation, did not put an exact timescale on his return but is expecting the 25-year-old to be sidelined for months.
"After such a good night at Anfield mine ended in the worst way! In the last minute one of my dreams collapsed," Jota posted on Twitter.
"I will be one more supporting from the outside, club and country, and fighting to be back as soon as possible."
Jota's absence adds to Liverpool's injury woes, with Luis Diaz also ruled out until after the World Cup in Qatar, which starts next month.
Joel Matip will also miss the visit of West Ham, but Trent Alexander-Arnold and Ibrahima Konate could be fit to return to the starting line-up.
Klopp was sent off late on in an emotional encounter with City for taking his protests towards the referee's assistant too far.
The German coach has so far not received a touchline ban from the Football Association and expects to take his place on the touchline on Wednesday.
"I think I will be there tomorrow because nothing happened yet," he said. "I don't think something will happen tomorrow a few hours before the game.
"I still think I should have dealt differently with the situation which I usually do. The whole game led to that a little bit. It was a very, very intense game with a lot of decisions we didn't understand on both sides.
"This for me was like the one drop that made the bucket overflow. I'm not happy with my reaction but that's the way it was and everybody saw it."
