The assault happened on Wessex Close, near to the junction of Culver Road, at around 12.30am on Wednesday January, 1.
A man and a woman, both in their 20s were assaulted with the man suffering a serious shoulder injury while the woman suffered injuries to her jaw, nose and teeth.
Police are appealing for witnesses to the incident.
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A spokesperson for Hampshire Constabulary said: “We are appealing for witnesses and information following reports of an assault in Basingstoke.
“Officers received a report that a man and woman, both in their 20s, were assaulted on Wessex Close, near to the junction of Culver Road, at around 12.30am on Wednesday 1 January.
“The man suffered a serious shoulder injury while the woman suffered injuries to her jaw, nose and teeth.
“Since this was reported to us, officers have been carrying out a number of enquiries and would like to appeal to the public for any information.
“Were you in the area at the time? Did you witness the incident or any suspicious behaviour? Do you have any dashcam, doorbell or CCTV images which could help our investigation?
“Anyone with information is asked to contact 101, quoting 44250002697.
“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”