Richard, 73, who was in Portugal when the search was carried out, has denyied any wrongdoing.
He has stayed at his Portuguese home since the search of the property in Berkshire, southern England, and was due to return to Britain next month.
"Sir Cliff was due to perform on 26 September at a charitable event in Canterbury Cathedral but doesn't want the event to be overshadowed by the false allegation and has therefore withdrawn," his spokesman said in a short statement.
"He is sorry for any disappointment or inconvenience caused."
In his denial last week of any impropriety, Richard 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."
Richard, one of Britain's longest-serving entertainers, was born Harry Webb in 1940 and in his early days was often seen as Britain's answer to Elvis Presley.
With his backing group The Shadows, Richard was one of Britain's most successful performers in the pre-Beatles era of the late 1950s and early 1960s and continued to have a string of hits over the decades.