Onlookers described how the woman leapt out of a blue Renault Clio near the junction with Hanover Street at around 6.30pm on Thursday.
Product designer Paul Pearson, 33, said he could hardly believe his eyes at the sight of the woman, who he described as in her early 20s, with shoulder-length black hair.
He said: "I stood there open-mouthed and she started laughing and screaming and ran up towards St Andrew Square. Once she went past I didn't want to stare so I kept on walking. Other people around just looked at each other." Police said they had received no reports of a streaker.