The incident is reported to have happened in the car park of Asda supermarket in High Street, Strood at around 8.30pm on Saturday, 7 November 2020.
A man in his 20s was shopping in the store when he was approached by a male who was being aggressive. The man then went to the carpark and the male reportedly assaulted him.
The victim sustained an injury consistent with a stab wound and was taken to a London hospital where his condition is described as serious but stable.
The suspect is described as being a black male, around 6ft 3ins tall, of skinny build with black hair in plaits. He wore a dark tracksuit and black trainers. He also wore a bag across his chest.
Officers are appealing for information and asking anyone who may have information to contact 01474 366149 quoting reference 46/200004/20.