Police fear the death toll in the accident that occurred on Friday afternoon may rise.
Madaripur Sadar Police Station OC Ziaul Morshed said almost half of the Barisal-bound bus sank into the canal after it fell off the bridge.
Police and Fire Service were trying to free a number of trapped passengers from the wreck.
The OC confirmed the death of five.
Fire Service officials said at least 25 persons were injured. They have been sent to Madaripur Sadar Hospital.