Both players were handed their first starts at the tournament in Qatar in the Selecao's surprise 1-0 defeat against Cameroon at Lusail Stadium on Friday.
However, Telles sustained his injury just four minutes after half time following a collision with Cameroon midfielder Andre-Frank Zambo Anguissa.
The Sevilla left-back - on loan from Manchester United - attempted to shake off his injury but he was eventually forced to withdraw in the 55th minute.
Arsenal's Jesus, meanwhile, was taken off in the 64th minute after complaining about a problem in his right knee.
According to Brazilian news outlet Globo, both players underwent scans after the defeat to Cameroon and the pair will now play no further part at the World Cup.
The report adds that Telles's injury is 'more serious' than that of Jesus, and there are fears that the 29-year-old may require surgery, with further tests set to be carried out to determine the severity of his problem.
Telles is now set for a lengthy spell on the sidelines and will not be fit to feature for Sevilla when the Spanish side returns to La Liga action against Celta Vigo on December 30.
Jesus, meanwhile, is set for up to a month on the sidelines, meaning the 25-year-old is a major doubt for Arsenal's final two Premier League fixtures of 2022 against West Ham United on Boxing Day and Brighton & Hove Albion on New Year's Eve.
Jesus could also miss the Gunners' first game of 2023 against top-four hopefuls Newcastle United on January 3 and the FA Cup third-round tie away at Oxford United six days later.
Brazil boss Tite is now having to contend with five injury problems within his 26-man squad, with Neymar, Danilo (both knee) and Alex Sandro (hip) also on the treatment table at present.
Neymar and Danilo sustained their injuries in the second half of Brazil's 2-0 opening group-stage win over Serbia, while Sandro picked up his problem in the 1-0 victory over Switzerland.
However, Selecao team doctor Rodrigo Lasmar has provided a positive update on all three players, who could recover in time for the last-16 clash against South Korea on Monday.
"Regarding Neymar and Alex Sandro, we think we have time on our hands and there is a possibility," Lasmar told reporters.
"Let's wait what their transition will be - they have still not started to train with the ball and it's something they will do tomorrow. It will be important to see how they respond to this new style, so depending on that, we will make a call."
Should Brazil beat South Korea in the round of 16, the five-time world champions will face either Japan or Croatia in the quarter-finals on December 9.