The Brazilian football confederation said the injury was not serious, adding Neymar left as a precaution and would be back in training on Wednesday (Thursday NZ time).
Brazil have been handed a huge disappointment after Neymar was taken out of their training session after just ten minutes.
However the 26-year-old forward has shown little signs of rust since returning for Brazil, scoring in consecutive friendlies on the eve of the finals.
Costa Rica's only World Cup victory against a team from South America was four years ago against Uruguay.
While Neymar played out 90 minutes of the Group E clash, he was on the receiving end of several tough tackles from Switzerland's players at the Rostov Arena.
Given the success of Switzerland's rugged approach, Neymar can expect more of the same against Costa Rica and Serbia with the pressure upped on Brazil to rediscover the form they showed in qualifying. Because of the number of fouls that he suffered in the last match he's felt some pain in his ankle, and that's why he's not training today. For Neymar or any other player for Brazil, the pressure is always there, this is expected.
Tite must hope the malaise that affected his key player - and, it must be said, many of his team mates - will lift before their next game against Costa Rica in St Petersburg on Friday.
They insisted the problem was not related to the fractured right foot that required surgery and saw Neymar miss the last three months of the club season for Paris Saint-Germain.
Mexican referee Cesar Ramos's handling of the Swiss tactics divided opinion among fans and commentators as some called for greater protection for one of the world's best players, while many believed Neymar was too quick to go to ground. "When he is on the field he helps us a lot".
"We want to win, it's a World Cup, but the coach is not going to play with the players' health".
This is the first time since the 1978 World Cup in Argentina that the five-time champions have not won their opening match.