It was reported that a man aged in his 20s was stabbed on Hereford Road at around 10.35pm on Monday 5 February 2018.
He was taken to hospital with serious injuries, which are not believed to be life-threatening.
A 23-year-old man from Weymouth has been arrested on suspicion of attempted murder and is assisting officers with enquiries.
It is believed the two men were known to each other.
An investigation is underway and officers are currently conducting CCTV and house-to-house enquiries.
Detective Sergeant Rhys Griffiths, of Weymouth CID, said: “I am appealing to anyone who witnessed the incident or who has any information that could assist with the investigation, to please contact Dorset Police.
“At this time, the weapon – possibly a knife – believed to have been used in the alleged assault has not been recovered. I would urge anyone who comes across such a weapon in the vicinity not to touch it but to please get in touch with us immediately.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk, via email email@example.com or by calling 101, quoting occurrence number 55180019095. Alternatively, contact Crimestoppers anonymously on 0800 555111 or via www.crimestopppers-uk.org.