The League One side, who are currently 13th in the table, lost for the sixth time in their last eight matches at Oldham on Saturday and that result has prompted the Cherries' board to make a change.
Bradbury, 36, joined Bournemouth as a player in 2007 and then succeeded Eddie Howe as manager when he left for Burnley in January 2011.
He led the club to the play-off semi-finals last season where they were beaten on penalties by Huddersfield.
A statement said: "Youth-team manager Paul Groves and head of youth Shaun Brooks will take charge of the first team until the end of the season, starting with Tuesday night's fixture at Stevenage.
"The club will make no further comment at this stage."