The reported confrontation is said to have occurred at half-time during Saturday's FIFA World Cup second-round match as the teams headed towards the dressing rooms, although communications director Rodrigo Paiva denies punching Pinilla.
He told the Lance newspaper: "There was pushing between the two sides. That always happens when everyone comes together. It was not an isolated incident and I did not punch anyone.
"It happens a lot and it has happened in other games too."
At a Rio de Janeiro press conference on Sunday, FIFA spokeswoman Delia Fischer said: "We can confirm there has been an incident and the disciplinary committee is currently analysing the matter."
Cagliari forward Pinilla came off the bench to rattle the crossbar towards the end of extra-time in Belo Horizonte. He missed Chile's opening penalty after the 1-1 draw as his nation suffered a 3-2 shootout defeat.
Brazil take on further South American opposition when they meet Colombia in Friday's quarter-final at Fortaleza.
