The 39-year-old joined the club in June 2014 and leaves the Bully Wee sitting eighth in Scottish League Two.
Ferguson had described their match with Annan Athletic as a must-win if they were to retain hopes of a promotion play-off place, but they lost 1-0.
And Clyde said in a website statement on Sunday: "The board has today reluctantly accepted the resignation of first-team manager Barry Ferguson."
The Cumbernauld side have not won a league match since November and have lost eight of their last 10 games in the division.
They are now 14 points behind Annan, who are fourth - the final play-off spot.
Ferguson offered his resignation immediately after the defeat at Galabank, but he had been asked to reconsider.
"Despite a welcome run in the William Hill 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," added Clyde's statement.
"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."
Capped 45 times, Ferguson skippered Rangers and also played for Blackburn Rovers, Birmingham City and Blackpool.
He had a short spell as caretaker manager with Blackpool before joining Clyde.
His team lost out in the promotion play-off final last season after a third-place finish, having ended up sixth in his debut campaign as a coach.
Ferguson told Clyde's website: "I want to wish the club all the very best in the future.
"I hope that it can go on and achieve its aim of reaching the play-offs this season."
Clyde have not revealed who will take over coaching duties but promised another statement ahead of Tuesday's league match against Montrose at Broadwood.
Former Scotland captain Barry Ferguson has resigned as manager of Clyde.