The Swedish coach replaced Ian McParland and signed a three-year contract at Meadow Lane.
A statement on the club’s official website said: “The club can confirm that first-team manager Hans Backe has resigned his position at the club.
“The club wishes to thank Hans for his service and wishes him all the best in the future.
“Dave Kevan has been appointed caretaker manager and will take charge of the league visit to Bournemouth next Monday.”