The former Cabinet minister suggested “an awful lot of police time” is being spent looking at “historic offences and all this malarkey”.
Mr Johnson, also a former mayor of London, said people “want to see officers on the streets”, and he backed increased use of stop-and-search tactics as a way to tackle knife crime.
But the senior Tory’s comments about historic cases were condemned by Labour MP John Mann.
He said: “Boris Johnson says investigating child abuse was a waste of money. Try telling that to my constituent whose rapist got 19 years after we pressured for the case to be reopened.”
Speaking on LBC Radio, Mr Johnson was asked whether police cuts had contributed to the problems on London’s streets.
He said: “Keeping numbers high on the streets is certainly important. But the question is where you spend the money and where you deploy the officers.
“One comment I would make is that I think an awful lot of the money, an awful lot of police time, now goes into these historic offences and all this malarkey - £60 million I saw was being spaffed up the wall on some investigation into historic child abuse and all this kind of thing.
“What on earth is that going to do to protect the public now? What the people want is to see officers out on the streets doing what they signed up to do.”
Labour Party chairman Ian Lavery said: “These disgusting comments are an insult to every survivor of child sex abuse.
“If Boris Johnson has even a little bit of decency he will now apologise to the victims and families of those who have suffered.”