"He has been punished for his misdemeanour in Bremen," Austria coach Marcel Koller told reporters. "But I need my best players and I do not want to do without his footballing qualities."
Arnautovic, who has had previous disciplinary problems for club and country, and team mate Eljero Elia were stopped for speeding in separate cars and their behaviour prompted the police to call for back-up.
The Dutchman has also been banned by Bremen.
Austria, Sweden and Ireland are level on eight points and battling to finish second in European Group C behind leaders Germany, who appear set to coast home in first place.
Sweden have played a game less than their two rivals. They visit Austria on June 7.