The incident happened near the park on Doric Avenue, Chineham, at around 4pm on Thursday January 2.
The man has been described as being black and of big, muscular build. He was wearing a navy blue coat with its hood up and black jogging bottoms.
Police say the girl, who felt in fear, then met her father and the man left the scene.
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Officers have been carrying out enquiries and reassurance patrols in the area since the incident was reported and police are appealing for witnesses to the incident.
A spokesperson for Hampshire Constabulary said: “We are appealing for witnesses and information following a report of a suspicious incident in Vyne Park in Chineham.
“Officers received a report that a man had followed a young girl near the park on Doric Avenue at around 4pm on Thursday 2 January.
“The girl, who felt in fear, then met her father and the man left the scene.
“The man has been described as being black and of big, muscular build. He was wearing a navy blue coat with its hood up and black jogging bottoms.
“We know this report will cause concern in the local community, however, our officers are taking the report extremely seriously.
“Officers have been carrying out enquiries and reassurance patrols in the area since the incident was reported to us. If you see an officer and have concerns, please speak to them. Please remain vigilant and continue to report any similar incidents to us.
“We would also like to appeal to anyone with information which may help with our enquiries. Did you see a man in the area matching the description above? Did you witness any suspicious behaviour?
“Do you have any dashcam, doorbell or CCTV footage that could help our investigation? Anyone with information is asked to contact 101, quoting 44250002188.
“You can also submit information to us online here: https://www.hampshire.police.uk/tua/tell-us-about/cor/tell-us-about-existing-case-report/
“Alternatively, you can contact the independent charity Crimestoppers 100% anonymously on 0800 555 111, or via their anonymous online form at crimestoppers-uk.org”