Pamela Taylor, 48, left her home in Broadfield Drive at around 11.55am yesterday, and was last seen near Tesco and Aldi in the town shortly after, police said.
"She hasn't been in touch with her family and her disappearance is out of character," the force said.
"Combined with the fact she doesn't have her medication, we are extremely concerned for her wellbeing."
Ms Taylor was described as white, around 5ft 8ins, of medium build, with long auburn hair.
She wears glasses, and was last seen wearing a brown cardigan, black leggings, a black jacket and black boots.
She also had a crutch with her.
Sightings can be reported by calling 101, quoting reference LC-2011006-1356.