The Brazil international sustained the injury midway through the first half of Thursday's Copa del Rey defeat of Getafe.
The club confirmed on their website: "Tests conducted on Friday morning have confirmed that Neymar has sprained peroneal tendons in his right ankle.
"He is expected to be out of action for three to four weeks."
The injury will rule the 21-year-old out of the forthcoming Primera Division matches against Levante, Malaga and Valencia, as well as the Copa del Rey quarter-final.
However, he is expected to be fit for the Champions League double-header against Manchester City, the first leg of which takes place in England on February 18.