Former defender Monk, who played for the club during their rise through the divisions to the Premier League and took over from Michael Laudrup as manager in February 2014, steered Swansea to a record eighth-place finish last season.
"The decision has been made very reluctantly and with a heavy heart," Swansea chairman Huw Jenkins said in a statement on the club's website (www.swanseacity.net).
"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."
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Monk earned plaudits for Swansea's 2014-15 campaign and this season began in encouraging fashion as they were among the early pace-setters, drawing with Chelsea on the opening day of the season and beating Manchester United at the end of August.
However, since beating United they have managed only one win in 11 league matches and are only one point above the relegation zone ahead of this weekend's trip to Manchester City.
"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," Jenkins added.
"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."
Monk joined fourth-tier Swansea on a free transfer from Barnsley in 2004 and was a key part of the defence as they earned three promotions and returned to the top flight for the first time in 28 years in 2011 when they beat Reading in the Championship playoff final.
He captained the club in all four divisions and made 270 appearances for the Swans before taking over as manager on an interim basis when Laudrup departed.
He was made permanent manager in May, 2014.
"We hope to appoint a replacement as soon as possible," Jenkins said.
Monk is the fourth top-flight manager to lose his job this season following Tim Sherwood (Aston Villa), Brendan Rodgers (Liverpool) and Dick Advocaat (Sunderland).
Rodgers, who was in charge of Swansea when they were promoted to the Premier League, is among the favourites to replace Monk.
(Reporting by Martyn Herman,; Editing by Neville Dalton)
