Liverpool full-back Robertson was seen remonstrating with the official, Constantine Hatzidakis, at halftime in Sunday's game and video replays appeared to show him brushing off the Scotland international and catching him with his elbow.
"PGMOL will not be appointing Constantine Hatzidakis to fixtures in any of the competition it serves whilst the FA investigates the incident involving the assistant referee and Liverpool defender Andrew Robertson at Anfield," it said in a statement.
Robertson was booked for dissent by referee Paul Tierney as the players walked off the Anfield pitch and down the tunnel at half-time.
Liverpool boss Jurgen Klopp had said after the 2-2 draw that he did not see the incident although he had heard "something happened".
"I heard the pictures speak for themselves. I cannot say more. I didn't see a bit of it," Klopp said.
Former Premier League referee Dermot Gallagher said the PGMOL would speak to the relevant parties to understand what happened.
"I think, without doubt, the PGMOL and (Chief Refereeing Officer) Howard Webb will speak to Hatzidakis, ascertain his view and thoughts and how he feels," Gallagher told Sky Sports.
"The FA have already said they will speak to him and Andy Robertson... It's just a matter of following the process."
Fulham striker Aleksandar Mitrovic received an eight-match ban and a £75,000 ($93,128) fine for confronting referee Chris Kavanagh and pushing him with his shoulder during their FA Cup loss at Manchester United last month.
Former Blackburn striker Chris Sutton said on BBC Radio that he advocated for a ban while Keith Hackett, another former Premier League referee, said Hatzidakis's career is in 'jeopardy'.
"The ban on Aleksandar Mitrovic wasn't long enough, so this has got to be the equivalent if he is found guilty," Hackett said.
