Scotland international Robertson was seen remonstrating with an official at half time and video replays appeared to show Constantine Hatzidakis brushing off the player and catching him with his arm.
"PGMOL is aware of an incident involving assistant referee Constantine Hatzidakis and Liverpool defender Andrew Robertson at half time during the Liverpool v Arsenal fixture at Anfield," Professional Game Match Officials Limited (PGMOL) said.
"We will review the matter in full once the game has concluded."
In a super-charged game, Liverpool fought back from two goals down to draw 2-2.
Asked about the incident, Liverpool manager Jurgen Klopp (55) said: "I didn't see it at all. I heard something happened. I heard the pictures speak for themselves but I don't know more."
