The ban means he will miss his team’s match against the Netherlands on Thursday in Amsterdam. Both teams won their opening games in Group C.
“We have to live with it,” Austria coach Franco Foda said. “There is nothing we can do.”
The incident flared after Arnautović scored Austria’s third goal in a 3-1 victory over North Macedonia on Sunday in Bucharest, Romania. He later apologized on Instagram for “some heated words” and said he was not a racist.
Foda said Arnautović “overreacted” after being provoked by North Macedonian players. He did not elaborate.
Alioski later said he had not heard what Arnautović said in Serbian. That left it unclear how UEFA could prove a charge of racism or ethnic discrimination.
“It’s a shame (for Austria) because he’s a very good player,” Netherlands coach Frank de Boer said.
The Albanian minority forms about a quarter of North Macedonia’s 2.1 million population.
Tensions between North Macedonians and ethnic Albanians in the small Balkan country erupted in 2001 when Albanians took up arms and fought with government forces, demanding more rights.