Club chairman Huw Jenkins told Swansea's official website the decision had been made "very reluctantly and with a heavy heart".
Monk's departure, though, is no surprise, given Swansea's miserable Barclays Premier League form
What turned out to be his last game in charge was a 3-0 home defeat against Leicester five days ago.
Monk took training as usual with the team on Tuesday, but his departure from the Liberty Stadium had been widely expected ahead of next Saturday's trip to Manchester City.
Swansea have won once in their last 13 games, and the Leicester defeat left them just one point above the Premier League relegation zone.
Monk guided the Swans to an eighth-place finish in the top-flight last season, but their form has nose-dived during this campaign.
Former Swansea manager Brendan Rodgers, who guided the Welsh club into the Premier League, is the bookmakers' favourite to replace Monk.
Reflecting on Monk's exit, Jenkins told the Swansea City website: "The decision has been made very reluctantly and with a heavy heart.
"To find ourselves in our current situation from where we were in the first week of September, and considering the drop of performance levels and run of results over the last three months, it has brought us to this unfortunate decision today.
"Garry took on the job 22 months ago with the backing of everyone at the club.
"And when you take into account the excellent campaign we had last season when we broke all club records in the Premier League, nobody foresaw the position we would be in at this moment in time.
"Bearing that in mind, and the current uncertainty around the club, we felt the situation needed clarity to move forward.
"It was not a decision we took lightly, especially given Garry's history and standing within the club.
"And it goes without saying that we wish Garry all the very best for the future and thank him for his tremendous service, not only as a player over the last decade, but also as our manager
He will always have a warm welcome at this football club."
Jenkins added that it was hoped to appoint a replacement "as soon as possible."
There is no news at this stage on the future of Monk's Swansea assistant Pep Clotet.
Source : PA
Source: PA