They lost at home to Wakefield on Sunday and have one point from their opening three games.
Assistant coach Willie Poching has been placed in temporary charge for Friday's home game against St Helens.
"The sole focus of everybody at the club at this time is on Friday's game and securing two much needed points," the club said in a statement.
"Any further comment on the situation, future plans and expectations will follow after the weekend," it added.
Chester, 37, was in charge for 18 months and led the club to last year's Challenge Cup final at Wembley, where they lost 50-0 to Leeds Rhinos.
He signed a three-year contract when he was appointed to replace Craig Sandercock in 2014.
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BBC Radio Humberside's Simon Clark
"Chris Chester was at pains last week to say that his side's game against Wakefield was not a must-win game. In the end it turned out it was and the defeat to his home-town club cost him his job.
"Chester's squad had suffered injury blows even before a ball was kicked in anger. Captain Terry Campese and Kevin Larroyer have yet to play this season and James Donaldson suffered a serious wrist injury in the Robins' second game which is likely to keep him out for 10 weeks.
"Attention now turns to Chester's replacement with former England coach Steve McNamara among those strongly tipped for the role."
Hull KR have sacked head coach Chris Chester just three matches into the Super League season.