The 45-year-old had overseen a poor start to the new Premier League campaign, with the Canaries picking up just two points from their first 10 games back in the top flight.
A 2-1 triumph away to fellow newly-promoted side Brentford on Saturday afternoon saw Norwich end their winless start to 2021-22 and move to within five points of safety, but it did not prove enough to save Farke's job.
In a statement announcing Farke's exit after four-and-a-half years at the helm, sporting director Stuart Webber said: "In continuing to demand the very best for our football club, this decision was not an easy one.
"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.
"All at Norwich City should be forever grateful to Daniel and his staff for the significant role they have played in our journey. 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.
"It's important that we now look forward. We have 27 league games remaining and a long way to go in the current season. We know we have the ability within our playing squad and staff to start picking up points and climbing the league table."
Farke took charge at Carrow Road in the summer of 2017 and went on to oversee 208 games as manager, winning 87, drawing 49 and losing 72.