The Dane is leaving the Premier League club after 20 months, having signed a new contract in March 2013 after being linked with leading clubs following his team's triumph in the League Cup.
Now, though, Swansea is 12th in the standings but just two points above the relegation zone, prompting the 49-year-old Laudrup's dismissal.
"It is a decision we have taken reluctantly," chairman Huw Jenkins said. "But it's a decision made in the best interests of Swansea City Football Club and our supporters. It is the first time in nearly 10 years that the club has parted with a manager in this way, but we had to remove the constant uncertainty surrounding the club and Michael's long-term future with us."
Garry Monk, the 34-year-old defender who has been out injured since September, 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 favoured by Swansea; Oscar Garcia, who currently manages 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 fierce rival Cardiff at the Liberty Stadium on Saturday.
"After thinking long and hard about the best way forward, I felt it was unlikely we would achieve a stable environment at the club (with Laudrup) to allow us to get back to basics and produce the performance levels that have served Swansea City so well over the last few years," Jenkins said.
"Now we need to put that uncertainty behind us and move forward as a united football club on all fronts."
For Laudrup, whose fortunes have rapidly plummeted since the League Cup success last February, it is the latest setback in a mixed managerial career for the former forward following a successful playing career that took in both Barcelona and Real Madrid.
After winning the league and cup in Denmark with Brondby, he guided Getafe to the final of the Copa del Rey — where they lost to Sevilla — in his one season with the unheralded Spanish club. Next came a troubled year in Russia with Spartak Moscow before returning to Spain with Mallorca, where he soon fell out with the owners.
It was at Swansea where his profile soared, building on the work of predecessor Brendan Rodgers and initially establishing the team as a fixture in the Premier League's top 10 with its attractive passing game.
But since beating lowly Bradford in the cup final, Swansea has won just eight of out 35 Premier League games across the two seasons and there have been continuous reports about a rift with the hierarchy.