The 56-year-old, who had been in charge for just 10 months, leaves Ashton Gate with the team currently 22nd in the Sky Bet League One table, having managed only two wins in 18 matches this season.
"We have given the situation as much time as we could to improve but have become increasingly concerned about the club's league position and have decided that a change of head coach will give the club the best possible chance of improving this," vice chairman Jon Lansdown wrote in an email to supporters.
"The league table does not lie. We are currently in the relegation zone and have been there for most of the season. This is not acceptable and the board feels that it needs to take action to try and rectify this; we need to move to ensure that results on the pitch keep up with progress off the pitch.
"It is vital that we now look to appoint a head coach who buys into our strategy and can help us to continue to grow and develop it successfully. This, of course, includes results on the pitch.
"This is an important decision and one which we will take careful consideration and diligence in making."
O'Driscoll oversaw just 11 victories during his 40 games at the helm of the Robins as they suffered relegation to League One and then struggled at the foot of the third tier.
Having gone 12 league games without a win, O'Driscoll oversaw two wins from three league games heading into November but a defeat to Sheffield United and draws with Tranmere and finally Leyton Orient on Tuesday proved to be his last matches at the helm.
John Pemberton will take charge of the first team for Saturday's visit to Preston.