The Canaries defeated fellow promoted side Brentford 2-1 away on Saturday but that was not enough to keep Farke in a role he had held since May 2017.
Despite their win, Norwich are bottom of the Premier League table with five points from eleven games.
In his time in charge of Norwich, Farke led them to two promotions from the Championship.
"In continuing to demand the very best for our football club, this decision was not an easy one,” Norwich sporting director Stuart Webber said in a statement.
"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."
Farke is the fourth managerial casualty of the season after Steve Bruce, Nuno Esperito Santo and Xisco Munoz.
Norwich will now look to appoint a new manager as they head into the international break and will host Southampton in their next Premier League game.
