The npower Championship side confirmed in a statement they had terminated the contracts of the Norwegian as well as assistant manager Johan Lange and first-team coach Patrick Weiser.
Solbakken's six-month reign at Molineux has been an unqualified failure, with the newly-relegated club 18th in the table and now the victims of one of the biggest upsets of the third round.
Wolves have won just three of their last 16 league games and the club branded that streak as "a hugely disappointing run of performances and results"
They have put Kevin Thelwell, head of football development and recruitment, in caretaker charge, assisted by development coach Steve Weaver.
Speaking after the match, Solbakken had said he was not "embarrassed" by the 1-0 defeat at Kenilworth Road and insisted he remained the man to "put it right" at the club.
But Wolves bosses have clearly taken a different view.