The French club say he will then be assessed to see whether surgery is required although Alves' spokesman said an operation was not needed.
The experienced full-back was hurt in the 80th minute of his side's 2-0 victory over Les Herbiers on Tuesday and, despite initially playing on, was eventually replaced by Thomas Meunier.
There may be time for him to recover, though, as Brazil play their first World Cup match against Switzerland in Rostov-on-Don on June 17, five and a half weeks away.
Any fears that Alves would miss out on Russian Federation 2018 have been allayed, however, as the right-back could be back before the end of the month, with Brazil's next friendly against Croatia coming on June 3.
Brazil play warm-up matches against Croatia on June 3 and Austria seven days later before heading to Russian Federation where they will face group rivals Switzerland, Serbia and Costa Rica.
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