The force worked with the BBC to broadcast live footage of officers searching the singer's house in August in connection with a historical allegation of sexual assault, which he denies.
The Home Affairs Select Committee says the agreement should never have been made.
Committee chairman Keith Vaz said: "No British citizen should face a situation where they see their homes being raided on live television.
"This has caused irreparable damage to someone who has not been arrested or charged with any offence and denies any wrongdoing."
South Yorkshire Police has apologised.
It said: "Whilst we believe our actions were within policy and were well intended, they were ultimately flawed and we regret the additional anxiety which was caused to Sir Cliff Richard.
"South Yorkshire Police has changed the way it deals with this type of media enquiry. In high-profile cases the force no longer provides privileged briefings to reporters, nor does it confirm information which media sources seek to verify.
"We are fully cooperating with the Metropolitan Police investigation regarding the original source of information."
Sir Cliff Richard's lawyers have also responded.
They said: "We feel that it is necessary to record that, leaving aside the actions of the police, the actions of the BBC have also caused very serious harm to our client at a time when he had not been interviewed by the police, or of course arrested or charged.
"Against this backdrop, we believe that it would be inappropriate to hold that the BBC has 'behaved perfectly properly', as suggested at the hearing of 2 September.
"As stated in our letter of 1 September 2014 we do not feel it appropriate to say more whilst there is a live investigation ongoing, but felt that it would be wrong not to place on record at this stage our concern regarding the BBC, whose coverage has led to immeasurable harm to our client and was both premature and disproportionate."
The BBC denies any wrongdoing. In a statement, it said: "The committee chairman has already said that the BBC acted 'perfectly properly' in handling this story, and we're pleased today's report confirms this."
Sir Cliff Richard has not been arrested and denies the historical allegations.