The 27-year-old, who is suspended for the Champions League last-16 second leg at Real Madrid on Wednesday, had a scan on Monday that showed meniscus damage.
The Ligue 1 club said in a statement that Bastos would fly to Brazil to be operated on this weekend by Edilson Thiele, one of the national team's surgeons.
"It is an inconvenience," coach Claude Puel said of the injury which came to light after the 2-0 win over Sochaux at the weekend.
"I am not a surgeon but we hope we can have him available towards the end of the season," he told a news conference at Real's Bernabeu stadium.
Real, seeking a place in the last eight for the first time since 2004, will have an advantage at the Bernabeu after they drew 1-1 in Lyon in last month's first leg.
However, the French side are something of a bogey team for the nine-times European champions.
Lyon knocked Real out of the competition at the same stage last season and the Spanish team have failed to beat the French side in seven meetings in European competition.
Puel said there was no point dwelling on past achievements, adding Real would start as favourites but that he liked his team's chances of scoring.
"Last year we had the aim of scoring and we did and this year we come to the Bernabeu with the same intention," said the 49-year-old former Monaco player and coach.
"We'll have to fight and play well defensively and we'll also have to destabilise the opposition.
"We have been playing very well but so have Real Madrid. It will be a match between two confident teams who have been on good form," added Puel.
