The Welsh outfit announced on Wednesday afternoon that Monk's 11-year stay with them had come to an end following a run of one win in 11 Barclays Premier League matches that has left them just one point above the relegation zone.
Chairman Huw Jenkins said in a statement on the club's website he hoped to bring in a replacement ''as soon as possible''
Former Swans and Liverpool boss Brendan Rodgers is among those being linked with the vacancy - although reports have suggested that reunion is unlikely to happen.
Regarding Monk, Jenkins said of the departure of the long-serving Swansea defender who took charge of the team in 2014: "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 (fourth in the table after beating Manchester United 2-1 on August 30), and considering the drop of performance levels and run of results over the last three months, it has brought us to this unfortunate decision."
Monk steered Swansea to an eighth-placed finish with a haul of 56 points last season and Jenkins added: ''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.''
Monk joined Swansea - then in League Two - as a player in 2004 and went on to captain the side, be a part of three promotion campaigns and win the Capital One Cup.
He made 270 appearances for the Swans, then took over as interim first-team boss in February last year following Michael Laudrup's departure.
Swansea were just two points above the drop zone at that time, but Monk kept them up and was handed the permanent job at the end of that season.
He subsequently led them to their best-ever Premier League finish last term and with this season beginning well, Monk was being touted as a future England manager.
However, Swansea's form has dropped off dramatically since and the 36-year-old now finds himself out of a job.
Source : PA
Source: PA