The 222 million euro striker was on Wednesday ruled out for 10 weeks to recover from an injury to the fifth metatarsal on his right foot.
He suffered the blow on 23 January at the Parc des Princes during PSG's 2-0 win over Strasbourg in the last 32 of the French Cup.
The same problem last season prevented him from appearing in the second leg of the last 16 against Real Madrid.
"After detailed analysis by specialists, a consensus was reached of a conservative treatment of Neymar's injury to the fifth right metatarsal," PSG said in a statement. "Informed of this recommendation,the striker agreed with this protocol. As a result, Neymar is expected to return to the field within 10 weeks."
If PSG manage to see off a resurgent Manchester United in the last 16, the 26-year-old could play in the first leg of the quarter-finals which are scheduled for 9 and 10 April.
Neymar has scored 20 goals this season in 23 appearances, including five in the Champions League group stage.
The extent of Neymar's injury comes as the Ligue 1 pacesetters fret over Marco Verratti's recovery from an ankle problem. They cannot call on the services of his fully fit fellow midfielder Adrien Rabiot.
The 23-year-old Frenchman has been distanced from the first team after refusing to sign a new contract.
However on Tuesday PSG signed the Argentine international midfielder Leandro Paredes from Zenit Saint Petersburg. They have also been linked with the Everton midfielder Idrissa Gueye.