Paiva, who is a well-known figure in Brazilian football, has admitted to shoving Pinilla during the interval of the round-of-16 clash, but said he only did so in self-defence.
FIFA’s disciplinary panel is understood to have access to video footage and pictures of the incident in Belo Horizonte.
"We can confirm there has been an incident and the disciplinary committee is currently analysing the matter,” FIFA spokeswoman Delia Fischer told a news conference in Rio de Janeiro.
A scuffle broke out as the teams headed to the dressing rooms at half-time after Brazil striker Fred slapped Chile defender Gary Medel on the back of the head as they walked off the pitch.
Brazilian media said Paiva and Chile assistant boss Sebastian Beccacece were involved in a confrontation which ended in the Brazil official punching Pinilla.
But Paiva denied allegations that he punched Pinilla.
"It was not just me. Pinilla came towards me and I just defended myself. I reacted by pushing him,” he told reporters.
Cagliari striker Pinilla came off the bench and nearly won the match for Chile in normal time but saw his shot in the last seconds of added time strike the crossbar.
Pinilla was one of three Chile players who missed penalties in the shoot-out which Brazil won 3-2 to progress to the quarter-finals.