The pair were involved in an embarrassing feud during PSG's 2-0 win over Lyon in September.
Cavani refused to let the world's most expensive player take a spot kick, having earlier argued over the taking of a dangerous free-kick.
Reports suggested that the duo's relationship got so bad that PSG even offered Cavani €1million to let Neymar take penalties.
However, the Uruguayan striker turned down the huge figure, meaning Emery has been forced to take action and hand the responsibility to Neymar himself.
'The coach has decided that Neymar will take the next penalty,' Cavani said, as reported by 'FourFourTwo'.
Cavani was speaking after PSG eased past Nantes 4-1 in Ligue 1 on Saturday, a game in which he scored a brace.