"We thank Andy for his contribution to the overall coaching set up at the club," chairman Chris Booy said on the club's website. (www.bristolrugby.co.uk)
"Unfortunately, the board lost confidence that Andy would retain the club's Premiership position, bearing in mind the results to date."
Robinson joined Bristol near the end of the 2012/13 season and, after losing in two Championship playoff finals, guided them to the top flight at the end of last season.
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Things have gone badly with a series of hefty defeats in the Premiership, where they have mustered just two bonus points, and two more in the European Challenge Cup.
"I am extremely proud to have played my part in helping Bristol Rugby reach their goal of getting back to the Aviva Premiership after a long seven-year absence," Robinson said.
"As everyone appreciates, the start of the season for Bristol Rugby has been extremely tough. However, I was surprised and disappointed by the board's decision.
"I would like to thank everyone involved with the club for some very special memories and wish them all the best for the future."
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
