Swansea part company with manager Laudrup
Defender Garry Monk has been installed as temporary head coach and he will be assisted by first-team coach Alan Curtis.
Laudrup departs with Swansea sit 12th in the Premier League, having won just once in their last 10 top-flight matches.
Swansea's most recent defeat came on Saturday against strugglers West Ham, with Monk set to make his managerial debut in the south Wales derby against Cardiff City on Saturday.
Former Mallorca, Getafe, Brondby and Spartak Moscow coach Laudrup moved to the Liberty Stadium in June 2012 and won the League Cup in his first season at the club, qualifying for the UEFA Europa League as a result.
While Swansea have been disappointing in the Premier League, they qualified for the knockout stage of the UEFA Europa League and will face Italian side Napoli in the round of 32 later this month.
Swansea chairman Huw Jenkins said in a statement on the club's official website: "It is a decision we have taken reluctantly.
"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.
"I had a meeting with Michael today (Tuesday) in a final attempt to support him and establish a way to improve the work of the backroom team to secure the results we need over the final 14 Premier League games.
"However, after thinking long and hard about the best way forward I felt it was unlikely we would achieve a stable environment at the club 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.
"Now we need to put that uncertainty behind us and move forward as a united football club on all fronts, while placing on record our gratitude to Michael for the work he has done over the last 18 months and wish him well for the future.
"I hope all our supporters can fully understand how difficult this period has been for us and I would urge everyone connected to the football club to get behind Garry Monk, the staff and players."