It happened shortly after 1pm yesterday (07/08) when the victim, who is in his 40s, was walking along Inglesham Road, Penhill.
The victim, who was aided by his wheeled frame as he is paralysed down his left side, fell to the ground after the attack, as his holdall bag was ripped off his shoulder by the suspect.
The victim hit his head on concrete after he fell to the ground, but thankfully did not require hospital treatment for his injuries.
The stolen bag contained shopping, including boxes of cigarettes.
The suspect is described as white, around 6ft tall, aged in his late teens or early 20s, and wearing a black baseball cap, black jacket and black trousers.
Inspector Colin Conway said: “This was a despicable crime on a vulnerable man, who has been left incredibly traumatised by this attack.
“I would urge anyone with information, including anyone who might know who the suspect is, or anyone who has been offered cigarettes for sale, to call us and help us with our enquiries.”
Anyone with information should call PC Jamie Brown, from Swindon Police on 101, quoting crime reference 54210076865. Alternatively you can call Crimestoppers anonymously on 0800 555111.