Atletico de Kolkata coach Lopez was accused of striking the Frenchman during an ISL fixture against Goa on Thursday by his opposite number Zico.
In a fractious affair that saw seven players cautioned as Atletico came from a goal down to win 2-1, Zico accused Lopez of hitting the former Arsenal man as the players left the field at half-time.
Both Pires and Lopez have been suspended and fined, with the World Cup winner to miss Goa's next two games while being hit with a Rs.500,000 punishment.
It means Pires will be out of action for the games against Pune City and Delhi Dynamos for what the ISL describe as a breach of rules relating to "Offensive Behaviour and Fair Play".
Lopez has been suspended for four ISL fixtures and fined the same figure for breaching the same rules for a second time having previously received a warning from the All India Football Federation.
Both parties have four days to lodge an appeal.