It is unclear what the investigation pertains to, but it seems that Hatzidakis is under scrutiny in some way.
PGMOL's decision to keep Hatzidakis away from any matches during the investigation is likely a precautionary measure to ensure the integrity of the game is not compromised.
It remains to be seen what the outcome of the investigation will be and if Hatzidakis will be able to resume his role as a match official.
Hatzidakis made contact with Robertson's chin after the Scotland international approached him at the end of the first half in Sunday's 2-2 Premier League draw with Arsenal.
An angry Robertson and several team-mates approached referee Paul Tierney, who booked Robertson.
Refereeing body PGMOL said it "will not be appointing Constantine Hatzidakis to fixtures in any of the competition" during the FA investigation.
Former Blackburn striker Chris Sutton told BBC Radio 5 Live on Sunday: "He has to be banned. He will have to sit out a number of games.
"You can't have assistants throwing elbows. I really don't know what he was thinking.
"I can't remember another incident like this. Where is the precedent for these things?"
Former Manchester midfielder Roy Keane described 28-year-old Robertson as a "big baby".
"He grabs the linesman first," Keane said on Sky Sports. "Robertson should be more worried about his defending. Just get on with the game."
PGMOL (Professional Game Match Officials Limited) said it would "review the matter in full".
