"Today is one of the most difficult moments of my career... and again in a World Cup," Neymar wrote on Instagram.
"I have an injury yes, it's annoying, it's going to hurt but I'm sure I'll have the chance to come back because I'm going to do my best to help my country, my team-mates and myself."
The Paris Saint-Germain star suffered ligament damage in the 2-0 victory against Serbia on Thursday when he collided with Serbia's Nikola Milenkovic.
The 30-year-old tried to continue but was substituted with about 10 minutes to go and underwent an examination on Friday.
Rodrigo Lasmar, the doctor for the Brazilian football federation (CBF), said Neymar would miss the match against Switzerland on Monday.
However, Brazil's Globo Esporte reported that he could also be sidelined for the final Group G game against Cameroon on December 2, but then would return if Brazil reach the knockout phase.
Brazil right-back Danilo will also miss Brazil's second game with an ankle strain.
"We will not have these two players for our next match but they continue their treatment with the aim of recovering in time for the rest of the competition," the doctor said in a video released by the CBF.
Coach Tite was optimistic after the Serbia match that Neymar would be back to lead Brazil's bid for a record-extending sixth World Cup crown.
"You can be certain that Neymar is going to play in the World Cup," Tite said, adding that the attacker had initially stayed on the pitch after hurting his ankle "because the team needed him".
Neymar's career has been peppered by injuries which have impacted on his previous two World Cups.
In 2014 he suffered a fractured bone in his back in the quarter-final win over Colombia, meaning he was sidelined when the hosts were thrashed 7-1 by Germany in the semi-finals.
Four years later he raced to recover from injury in time for the tournament in Russia, but Brazil never hit the expected heights before losing to Belgium in the last eight.
