The former Stoke and West Ham frontman, who is currently playing his football in China with Shanghai Port, was restrained by skipper David Alaba as he gestured angrily after scoring late in Sunday's 3-1 Group C victory in Romania
A UEFA statement said: "In accordance with the Article 31(4) of the UEFA Disciplinary Regulations, an Ethics and Disciplinary Inspector has been appointed to conduct an investigation regarding the incident involving the player Marko Arnautović that occurred during the 2020 European Championship group-stage match between the national teams of Austria and North Macedonia on 13 June 2021.
"Further information on this matter will be made available in due course."
The incident came in the 89th minute of the game at the National Arena in Bucharest when, after beating North Macedonia keeper Stole Dimitrievski, Arnautovic, who is of Serbian heritage, appeared to make comments towards opposition players and then turned towards spectators.
Reports have alleged his initial remarks were aimed at defender Egzon Bejtulai and Gjanni Alioski, who both have Albanian roots.
Arnautovic later apologised for his outburst, but insisted he was not a racist.
In a post on his official Instagram account, he wrote: "There were some heated words yesterday in the emotions of the game for which I would like to apologise - especially to my friends from North Macedonia and Albania.
"I would like to say one thing very clearly: I am not a racist. I have friends in almost every country and I stand for diversity. Everyone who knows me is aware of that."