The 37-year-old worker from Rosebud suffered non-life threatening injuries and was airlifted to The Alfred hospital in a stable condition.
A 25-year-old Rosebud man was arrested several hours later and was assisting police with their inquiries.
The retail union, SDA, said officials were talking to store management about what happened.
“Anyone who participates in violence against retail workers should feel the full force of the law,” it posted online. “Our members deserve to feel safe and respected at work.”
Woolworths Victoria general manager John Di Tirro said the company was helping the police investigation.
“There is no place for violence like this anywhere in our community,” he said.
“Our thoughts are with our team member and his loved ones at this difficult time and we’ll be offering them our full support.”
The store remained closed on Thursday evening.
Tuesday’s stabbing came after a supermarket worker was assaulted in Brunswick on Sunday.
It is alleged the offender struck a staff member at the Barkly Street shopping centre with a stick shortly before 8.30pm.
A police spokeswoman said the staff member did not require medical treatment, but a passerby who intervened did suffer minor injuries.
The alleged attacker, a 43-year-old man, was later charged with recklessly cause injury, unlawful assault, assault with a weapon and possess a dangerous article.
He was bailed to face Melbourne Magistrates Court on July 30.
There is nothing to suggest either incident was connected to panic buying.
Anyone with information is urged to contact Crime Stoppers on 1800 333 000.
Erin covers crime for The Age. Most recently she was a police reporter at the Geelong Advertiser.