The 29-year-old woman was had been walking her dog on a field behind Pale Meadow Road, near to Severn Street when her dog approached a man's dog, police say. Both animals were off-lead their leads.
The man's dog, a white bichon frise, appeared to be scared of the victim's dog.
The white bichon frise's owner, who was accompanied by a woman, then took what is thought to be a baton and threatened the victim.
He shouted at the victim and then allegedly threatened to hurt her dog.
The duo then walked off in the direction of Pale Meadow housing estate.
It happened at about 1pm on Saturday, March 12.
The offender is a white man believed to be in his 50s, of a medium build with short grey, swept back hair.
The woman who was with the man is described as white, with shoulder length grey/blonde hair. It is believed she was also in her 50s and was wearing glasses.
Anyone with information is asked to call police on 101, quoting incident 377S of march 12. Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org