"In continuing to demand the very best for our football club, this decision was not an easy one," said Norwich sporting director Stuart Webber.
"I know how determined Daniel and his staff were to succeed at this level, but we feel that now is the right time for a change to give ourselves the best opportunity of retaining our Premier League status."
Norwich's win meant they remained bottom of the table on goal difference with five points from 11 games.
In 2020 they were relegated after one season back in the top flight, finishing bottom, but the club stuck by Farke and he guided the Norfolk team back into the elite.
"All at Norwich City should be forever grateful to Daniel and his staff for the significant role they have played in our journey," Webber continued. "They helped deliver two Championship titles, many memorable moments and they all fully bought into our philosophy and what it means to be part of this football club.
"Daniel and his staff will always be welcome back here. I'd like to take this opportunity to thank them all for their hard work and wish them well for the future."