It comes after Uruguay's Alvaro Pereira continued playing after he was knocked unconscious in the win over England.
FIFpro wants players suspected of being concussed to be temporarily substituted so they can be assessed by doctors.
The players' union has accused Fifa of failing to protect the 28-year-old midfielder and wants its own medical team at games to make assessments.
Pereira was knocked out during England's 2-1 defeat by Uruguay in Group D of the 2014 Fifa World Cup on Thursday and the result leaves Roy Hodgson's men on the brink of an early exit.
Pereira admitted he was briefly unconscious but insisted he had wanted to continue after arguing with his team doctor.
"I said sorry a thousand times to the doctor because I was dizzy," the Sao Paulo player said. "It was that moment with your adrenaline flowing in your body, maybe without thinking what I really wanted to do was to help get the result.
"What really matters is that everything is okay. Nothing happened. It was just a scare."
The incident has echoes of Tottenham goalkeeper Hugo Lloris being allowed to play on despite suffering concussion in a game against Everton last season.
The incident even raised questions in the House of Commons were "horrific", the House of Commons when Labour MP Chris Bryant said it was now up to Parliament to provide "a lead" on whether sports stars should be allowed to continue playing, after Spurs manager Andre Villas-Boas failed to immediately substitute the injured goalkeeper.
Lloris was knocked unconscious in an accidental collision with striker Romelu Lukaku in a goalless Premier League draw.
Controversially, Villas-Boas (who was sacked later in the season) allowed Lloris to remain on the field of play for the remaining 12 minutes of the game.
There was a strong backlash against the incident but the Portuguese manager insisted he stood by the decision.