Werder had temporarily banned the pair on Friday but decided to extend the sanction to all training sessions and matches until the end of the season, after the late-night incident.
Arnautovic, who has had previous disciplinary problems for club and country, and Elia were stopped for speeding in separate cars and their behaviour prompted the police to call for back-up.
No alcohol was involved.
"In the final stretch of the season we need all players to be fully focused," the club's sports director Thomas Eichin said in a statement.
"We have made it clear to Marko Arnautovic and Eljero Elia that their behaviour damaged the team in this phase. Both will train separately until the end of the season."
Werder Bremen's 32-year stay in the Bundesliga is under increasing threat after they extended their winless sequence to 10 games following a 1-0 defeat to Bayer Leverkusen on Sunday.
The northern club are just two points above Augsburg who occupy the relegation play-off spot with three matches to play.
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