His exit follows a disappointing run of results, including a 1-0 home defeat by Dunfermline on Saturday.
Following the match, a group of fans protested outside the main entrance of the stadium, asking for Calderwood and chairman Rod Petrie to go.
Calderwood managed just 12 wins in his 49 matches at the helm of the Scottish Premier League outfit.
Hibs issued a brief statement, with Petrie saying: "The board decided that it was in the club's best interests to find a new manager to take Hibernian forward."
The club hold their AGM on Tuesday. It was on the morning of last year's meeting when they decided to depose the previous manager, John Hughes.
Calderwood, 46, was assistant to Chris Hughton at Newcastle United before joining Hibs on a three-year contract in October 2010.
A former Scotland international defender who played for Tottenham and Aston Villa, Calderwood started his managerial career at Northampton town in 2003, moving on to Nottingham Forest three years later.
His spell at Forest ended in 2008 and he joined the coaching staff at Newcastle the following year.
Over half of his matches in charge of Hibs - 26 - ended in defeat, including a Scottish Cup exit at the hands of Ayr United, then a Second Division side, in January.
Calderwood was linked with moves to Birmingham City and Forest during the summer when respective new managers Hughton and Steve McClaren were looking for assistants but no move materialised.
Hibs have had seven permanent managers in 10 years with Calderwood, Hughes, Mixu Paatelainen and John Collins each lasting less than two years in the hot-seat.
And that turbulent record has led to criticism of Petrie's handling of the Edinburgh club.
"Rod Petrie has to consider his position," former Hibernian midfielder Paul Kane told BBC Scotland. "In any other business he would have left before now.
"The board had to listen to the fans because attendances at Easter Road were dwindling.
"I'm sure Saturday's demonstration and the timing of the AGM played their part in this decision.Petrie has attracted flak from disgruntled Hibernian supporters
"I'm not surprised Colin Calderwood has left. The frustration among fans was evident."
Following the limp defeat to Dunfermline, Calderwood said: "It's a shocking result for us and we take the blame for it.
"We played below par as a team and too many individuals played nowhere near it."
Winger Ivan Sproule, who appeared as a second-half substitute against the Pars, said he was "embarrassed" after the loss.
"It's a poor situation we're in at the minute," added the Northern Ireland international. "It's hard to put into words.
"Where do you go? Where do you start picking positives?"