The Austria striker, who has attracted more attention for his antics off the pitch than his talented game since joining Bremen in 2010, was sent off in the 78th minute for stepping on Sergio Pinto in their 3-2 defeat.
Arnautovic, who was briefly banned from his national side earlier this year for fighting with team mates and was also suspended by his club for a while, had scored Bremen's first goal in the game just before the break.
"Marko Arnautovic is banned for three games for rough play," the DFB said in a statement.
The 22-year-old managed only three goals in 25 Bundesliga appearances for Werder last season - two of them in his second game - having joined the club after an equally problematic season with Inter Milan before that.
This season looked until now to be better with his goal at Hannover being his third of the campaign.
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