The Dane, who signed a new contract last March, is leaving the Premier League club after 20 months. Swansea (6-12-6) is 12th, two points above the relegation zone.
Garry Monk, a 34-year-old defender who has been sideline since September with an injury, will replace Laudrup, alongside current first team coach Alan Curtis, "for the foreseeable future," Swansea said.
Like Laudrup, two possible contenders for the job on a full-time basis are former Barcelona players who advocate the type of passing game favored by Swansea; Oscar Garcia, who currently manages the second-tier club Brighton, and Luis Enrique, who is in his first season as coach of Celta Vigo.
Swansea's next game is the south Wales derby against frival Cardiff at the Liberty Stadium on Saturday.