Police said the man entered G101 store, in the town's Main Street, and demanded cash.
He fled with around £200, after the incident at 5.15pm on Tuesday.
The 35-year-old worker was not injured, but police said she had been left "very upset" by the incident.
As the man fled the shop, a female customer came in and passed him.
Moments later, as he made off along Main Street, he was chased by a man who saw him leaving the shop. Officers have urged the two witnesses to come forward.
Detective Sergeant Ian Connelly, from Cambuslang CID, said: "The area around the G101 store is usually fairly busy at this time of day with pedestrians and drivers.
"I would appeal to anyone who saw a man matching the description of the suspect to get in touch.
"I am particularly keen to speak to the woman who walked into the shop as the suspect was fleeing and also the man who ran after the suspect along Main Street."
The suspect is described as white, between 35 and 40 years old, and around 5ft 5in tall.
He was wearing a dark jacket, black hat, scarf and gloves, light blue jeans and white trainers.
Officers are reviewing CCTV images in an effort to find the suspect.
Anyone with any information is asked to contact Cambuslang CID on 101.