"Alex took on a very difficult task last season and did a fantastic job. He has our thanks for that," Bremen chief executive Frank Baumann said in a statement.
"He has all the qualities of a successful coach, and I'm sure that he will continue his path with success elsewhere."
Nouri, who was appointed manager in October last year after a short stint on an interim basis, led the side out of the relegation zone to an eighth-placed finish last season.
The 38-year-old becomes the third Bundesliga coach to be sacked this term after Andries Jonker (Wolfsburg) and Carlo Ancelotti (Bayern Munich).
Bremen's Under-23 coach Florian Kohfeldt will take charge of the first team for Friday's league match against 10th-placed Eintracht Frankfurt.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
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