Police Scotland are seeking witnesses to the incident in the Homebase car park at about 11.15 am last Friday, October 27.
At that time, a suspect described as around 50-years-old, with short grey hair, wearing dark-coloured clothing and of medium build became involved in a dispute over a car park space with the pensioner.
During the dispute, the suspect knocked the man to the ground, leaving him requiring stitches to a head wound.
The suspect was not known to the victim, and following the assault left the scene in what is believed to be a small blue or silver car.
As a result of the alleged assault the victim needed treatement at Dumfries and Galloway Royal Infirmary.
PC Sandy Currie at Dumfries said: “This appears to be an unprovoked assault on a 70-year-old man over a parking space.
“The attack has resulted in the victim being left with a cut to the head which required him to attend hospital for treatment.
“I would ask that anyone who witnessed the assault or knows the identity of the suspect involved to contact police on the 101 number.”