Hill, who took over at Bristol in July 2003, didn't travel to Edgeley Park for that game with the Sharks, with Paul Hull looking after team matters.
It is Hull who replaces Hill as head coach, with the former Bristol and England full back hoping to prevent relegation to the national leagues.
"We had already agreed with Richard that he would be leaving the Club at the end of the season but given the position we are in believe it to be more appropriate for Richard to leave now and for Paul Hull to take over as head coach," said Bristol CEO Steve Gorvett.
When Hill joined Bristol the side were in National One but the ex-England scrum-half guided them back to the top flight in 2004/05 and has since enjoyed four seasons in the Guinness Premiership.
Under Hill, Bristol reached the Premiership semi-finals in 2006/07, losing to eventual winners Leicester Tigers.
"Richard joined the Club when we had just been relegated and quickly built a team for the first season in the First Division and obtained promotion the following season," said Bristol Rugby chairman Chris Booy.
"Particular highlights of Richard's time as head coach would be surviving our first year in the Guinness Premiership, finishing third the following season and then competing in the Heineken Cup.
"I would like to thank Richard for all that he has done for the Club and wish him well for the future."