Paris Saint-Germain have confirmed the forward injured a metatarsal in his right foot during their 2-0 French Cup win over Strasbourg on Wednesday.
Neymar, 26, left the pitch after twisting his foot.
PSG said initial examinations revealed a “reactivation of the lesion of the fifth right metatarsal”.
The club added that the treatment would depend on how the injury heals in the next few days.
Neymar had fractured the same metatarsal last February and required surgery that effectively ended his club campaign.
He returned to action in May, in time for the World Cup in Russia.
PSG manager Thomas Tuchel said: ”Neymar is worried, because it’s the same foot, the right foot, in the same area.
Tuchel also criticised the match official for not protecting the Brazilian when Strasbourg’s players repeatedly fouled him.
“The referee didn’t whistle on one occasion, then two, then three and after that he ended up twisting his foot,” he added.
Manchester United host PSG at Old Trafford for the first leg of the Champions League round of 16 clash on February 12.
PSG, who enjoy a 13-point lead in Ligue, return to league action on Sunday when they host Rennes.
Meanwhile, French football expert Julien Laurens believes Ole Gunnar Solskjaer’s United will be a much trickier proposition for Tuchel and co than under Jose Mourinho.
“A lot has changed since the draw was made,” Thomas said.
“Solskjaer coming in, United on that great run of form. How much are PSG sitting up and paying attention to this?”
And Laurens says PSG know affairs are in much better order at Old Trafford now Mourinho has gone.
“Very much so,” he replied.
“I think that they can see since Mourinho has departed things are much better at United.”