The Christian singer's home in Berkshire was searched by police after a warrant was granted.
The 73 year old was not present when officers arrived.
Det Superintendent Matt Fenwick from South Yorkshire Police said: "A search warrant was granted after police received an allegation of a sexual nature dating back to the 1980s involving a boy who was under the age of 16 at the time."
It's thought a number of items were removed from the property.
The search is not part of Operation Yewtree but police from that operation have been informed.
It's being reported that the alleged incident took place at Sheffield United's Bramall Lane stadium in South Yorkshire during a rally headlined by American Evangelical Christian Billy Graham.
In a statement today Sir Cliff said: "For many months I have been aware of allegations against me of historic impropriety which have been circulating online. The allegations are completely false.
"Up until now I have chosen not to dignify the false allegations with a response, as it would just give them more oxygen.
"However, the police attended my apartment in Berkshire today without notice, except it would appear to the press.
"I am not presently in the UK but it goes without saying that I will co-operate fully should the police wish to speak to me.
"Beyond stating that today's allegation is completely false it would not be appropriate to say anything further until the police investigation has concluded."
Sir Cliff, has spoken about his strong Christian faith several times in the past.
In 2013 he told Premier: "Sometimes a Christian life can start that way, that you take the step, you don't feel any difference but somehow or another because you've taken the step God is already taking action in minor ways i suppose."
During an interview in 1968 he outlined where his Christian faith had come from: "It wasn't that a particular sermon hit me or anything like that.
"I'd spent a lot of time reading the New Testament and things came over to me gradually.
"I know now Christianity definitely involves something more than just believing in a God," he said.
The star is one of the most successful British musicians of all time selling 21.5 million singles during his career.
His hits include The Millennium Prayer, Sing a Song of Freedom and Congratulations.