Arnautovic, who was involved in several disciplinary problems for club and country before joining Werder in 2010, and Elia have been banned from training with the struggling Bundesliga outfit.
"We cannot use such unprofessional behaviour during preparation for our game at Bayer Leverkusen (on Saturday)," said coach Thomas Schaaf.
The duo were stopped for speeding in separate cars and their behaviour prompted a call for back-up, police officials said. No alcohol was involved.
Werder, who have failed to win their last nine league games, are in 14th place, five points above the relegation playoff spot with four matches left this season.