Paiva, a well-known figure in Brazilian football, admitted shoving Pinilla but said he only did so in self-defence.
A Fifa spokeswoman told a news conference in Rio: “We can confirm there has been an incident and the disciplinary committee is currently analysing the matter.”
The disciplinary panel is believed to have access to video footage and pictures of the incident in Belo Horizonte. A scuffle broke out as the teams headed to the dressing rooms in the Mineirao Stadium, sparked by Brazil striker Fred slapping Chile striker Gary Medel on the back of the head as they walked off the pitch.
Brazil media said Paiva and Chile assistant boss Sebastian Beccacece were involved in a confrontation which ended in the Brazil official punching Pinilla.
Paiva told reporters there was widespread pushing between the two squads, and said: “It was not just me. Pinilla came towards me and I just defended myself. I reacted by pushing him.”
Pinilla, who plays for Italian side Cagliari, came off the bench and nearly won the match for Chile but his shot in the last seconds of the match struck the crossbar. The striker was then one of three Chile players to miss penalties in the shoot-out which Brazil won 3-2 to go through to the quarter-finals.