The story or myth is found on various biographies of Oliver Cromwell notably

Through Great Britain and Ireland With Cromwell by children's history author Henrietta Elizabeth Marshall

There is a story told—I will not say that it is a true one—of how, one day, when Oliver was still a baby, he had been taken to see his grandfather. He lay asleep in his cradle, and his nurse must have been careless, for he was left all alone. As he lay there, a monkey came lolloping into the room and right up to the cradle. The monkey thought that the baby would be a lovely plaything, so he seized him and ran away with him. Leaping, swinging, clinging with hand and tail, he swung himself and his prize up to the flat lead roof of the house. Soon the baby was missed, and when it was discovered that the monkey was playing with him on the roof, the whole household was thrown into a state of confusion. Beds and blankets were brought out and placed on the ground, to catch the baby, in case the monkey should drop or throw him down. But the monkey was careful, and presently he brought Oliver safely to the ground again. So the baby was saved to grow up to be a great man.

and again in this chapter on the Civil War

The man who became Lord Protector was nephew to the Sir Oliver Cromwell who owned Hinchingbrooke.It is said that as a child he was taken by a pet monkey and carried to the roof of Hinchingbrooke. It is also said that he met the young Charles at Hinchingbrooke and gave him a bloody nose.

Now I must quote straight from Ted Vallance's website -someone who has spent a lot of effort researching this - and has a dedicated blogpost "Oliver Cromwell and the Monkey"

I wondered how old that particular story was. Thomas Cromwell’s Oliver Cromwell and His Times (1822) lists the story as one of the many extravagant claims inserted into hostile biographies of his ancestor (referring here to Mark Noble’s Memoirs of the Protectoral House of Cromwell (1787)) Noble claimed that he received this story – and the other familiar one of the young Oliver coming to blows with a young Charles Stuart – from ‘the rev. dr. Lort’s M.S.S.’ (Perhaps Michael Lort, the Georgian antiquary?) who in turn received this from ‘Mr. Audley’ (the non-juror Edward Audley).

The exact passage on Google docs quotes the original incident thus

His very infancy," says Noble, if we believe what Mr. Audley, brother to the famous civilian, says he had heard some old men tell his grandfather, " was marked with a peculiar accident, that seemed to threaten the existence of the future Protector: for his grandfather, Sir Henry Cromwell, having sent for him to Hinchinbrooke, (near Huntingdon, the ancient family seat) when an infant in arms, a monkey took him from his cradle, and ran with him upon the lead that covered the roofing of the house. Alarmed at the danger Oliver was in, the family brought beds to catch him upon, fearing the creature's dropping him down; but the sagacious animal brought the ' Fortune of England' down in safety: so narrow an escape had he, who was doomed to be the Conqueror and Sovereign Magistrate of three mighty nations, from the paws of a monkey."

So in conclusion, there is an anecdote and an original reference point for the anecdote - but whether it was true or not is still debatable

Furthermore, Andrew Barclay delves in some more and offers this comment on Ted Vallance's website to dig down the source of this tale