Bremen have drawn five and lost five of their 10 league matches this season, with a total of five points leaving them in 17th position in Germany's top flight.
Sunday's 3-0 home defeat to Augsburg was the final nail in the coffin, and Nouri, who only took the position in September 2016, has been relieved of his duties.
"Alex took on a very difficult task last season and did a fantastic job. He has our thanks for that. He has all the qualities of a successful coach, and I'm sure that he will continue his path with success elsewhere," Bremen sporting director Frank Baumann told the club's official website.
Nouri's assistant Markus Feldhoff has also lost his job, meaning that Under-23 boss Florian Kohfeldt will take control of first-team affairs for the Bundesliga clash with Eintracht Frankfurt on Friday.