At 10.10am, a 24-year-old woman was walking along Moggs Mead, towards Pulens Lane, when a man approached her.
He stopped in front of her, dropped his trousers and exposed himself, making a lewd comment. He then ran off.
Officers have released an e-fit of the man, who is described as white, aged between 35 to 40, of slim build and around 5ft 8ins.
He has messy brown hair, a scar on the left side of his face, either below or above his eye and was wearing a navy blue, heavy cotton coat and stonewashed blue jeans
He spoke with a Portsmouth accent.
PC Mark Baker, from Alton police station, said: "This was a rare occurrence, and I would like to reassure the community that we are working hard to identify this man.
"Anyone who recognises the person in the e-fit, or has seen someone matching his description in the area, should contact police."
Anyone with any information should contact PC Baker at Alton police station on 0845 045 45 45 or Crimestoppers anonymously on 0800 555 111.