The 39-year-old joined the Bully Wee in June 2014 and led them to the playoff final last season.
However, the former Rangers man leaves them sitting eighth in the fourth tier and without a league win since November 19.
A Clyde statement said: "The board has today reluctantly accepted the resignation of first-team manager, Barry Ferguson.
"Despite a welcome run in the Scottish Cup, which ended with an agonising defeat to Championship side Ayr United in a fifth-round replay, both the manager and the club were disappointed with the recent poor run of league results, often not reflecting the effort and standard of play, which culminated in the defeat at Annan yesterday.
"That result leaves the club with only an outside chance of achieving the objective of securing a play-off place and then promotion to League One.
"The club would like to thank Barry for his unstinting commitment to the job over the last two and a half years and wishes him every success in the future."