Jurors concluded the 96 victims of the 1989 disaster were unlawfully killed and there were police failings.
Shadow Home Secretary Andy Burnham said "those responsible must be held to account" saying the force had gone back on its 2012 apology.
The force's Police and Crime Commissioner said there had been an "erosion of trust".
Dr Alan Billings said he had no choice but to act.
The PCC said: "The continuing criticism that has been directed at the Chief Constable and the eroding trust and confidence in South Yorkshire Police I have been left with no choice other than to suspend David Crompton from his duties.
"I have reached this decision with a heavy heart following discussions with David."
Mr Crompton was due to retire in November after four years in the role.
Thousands of people are attending a vigil in Liverpool in memory of those who died in the Hillsborough disaster.
Mr Burnham, who has backed the campaign for justice for the Hillsborough victims, had called for Mr Crompton's resignation in the House of Commons.
He said the force had gone back on its 2012 public apology following the release of the Hillsborough Independent Panel report.
Mr Burnham said: "Shamefully, the cover-up continued in this Warrington court room. Millions of pounds of public money were spent retelling discredited lies.
"Lawyers for retired officers threw disgusting slurs; those for today's force tried to establish that others were responsible for the opening of the gate.
"If the police had chosen to maintain its apology, these inquests would have been much shorter."
Lawyers acting on behalf of the 22 of the families welcomed the suspension.