The 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.
The club are now looking for their fourth boss in less than a year after the departure last February of Mick McCarthy and the brief tenure of Terry Connor.
Solbakken, 44, joined the club last summer following his dismissal by German side Cologne.
The former Wimbledon midfielder, who was once pronounced clinically dead after suffering a heart attack in training which forced his retirement from playing, had won five Danish titles in charge of Copenhagen.
His Wolves side have lost all four of their matches since Christmas, though, and the club have acted quickly in a bid to avoid becoming embroiled in another relegation battle, this time to the third tier.
- Sports & Recreation