Detectives were called to Zap Fitness on Hobart Road just after 1pm Wednesday.

The offender had fled the scene, and police spent the afternoon searching nearby streets and a home.

The victim was "going about his daily business", when he was attacked.

Detective Inspector Craig Fox said the stabber had turned up briefly at the Launceston General Hospital on Wednesday afternoon with a minor injury, but had not been located by police.

The victim remained at the LGH, having suffered non-life-threatening injuries.

"Our information is the men were not known to each other," Detective Inspector Fox said.

"The victim was just a man going about his daily business, but the good thing is he is likely to recover, but a very traumatic experience."

The suspect has been described as being in his late 40s, about 172 centimetres tall, with grey receding hair, a grey beard and wearing a green Everlast top, possibly with blood stains.

While police have warned not to approach the man, Detective Inspector Fox said the "public was very safe".

"When any incident like this happens it is definitely concerning, the public need to be aware of this gentleman," he said.

"This is an unprovoked attack ... we will be looking at whether this person has some mental health issues that need to be addressed, but at this stage the public is very safe.

"It wasn't a prolonged attack... it seems to be a random act of violence."

A weapon was recovered at the scene.