The 22-year-old, signed by Bremen for six million euros (8.5m US dollars) in July, has been dropped without the club specifying his offence and his team still not sure of their Bundesliga survival.
According to Bild sports daily, Arnautovic was out nightclubbing on Thursday to the early hours of Friday morning.
"We need total concentration against Dortmund and with Marko that was not the case," Bremen coach Thomas Schaaf told German daily Bild.
The former Inter Milan and FC Twente star has scored just two league goals in 24 appearances this season and has already fallen foul of club bosses.
Schaaf was left fuming at yet another poor performance from Arnautovic in last Saturday's 1-0 defeat to Wolfsburg and said the Austrian must give the team more.
And Arnautovic was warned back in August to improve his attitude, just a month after joining the north German side, because of a lack of effort in training and in matches.
Short link: