Patrol police were called to the scene, at the intersection of Pattana Rd and Wirat Hongyok Rd, at about 7pm.
Officers arrived with Kusoldharm rescue workers to find a blue Honda Fino on the road with a man, later identified as Panupong Saetae, 28, from Phuket, bleeding on the road nearby.
Mr Panupong was taken to Vachira Phuket Hospital.
One witness told The Phuket News, “The man [Mr Panupong] was driving his motorbike on Wirat Hongyok Rd when two men on another motorbike pulled up alongside.
“They stopped by the side of the road and were arguing about the motorbikes clipping each other. After that they started fighting.
“One of the two men took out a knife and attacked him [Mr Panupong] with it. Local residents tried to stop them, but the two men sped away,” the witness added.
Police notified other patrol officers across the town to keep a lookout for the two suspects, but failed to catch them.
Police are continuing their investigating and will check CCTV in the area in the hopes of tracking down the suspects, officers said.