The Saugeen Shores Police Service (SSPS) responded to an incident at a Port Elgin grocery store on Thursday evening.
Police said they received a call about a man who was allegedly threatening people and causing damage, just after 8 p.m.
In a statement, SSPS said the incident started when a man and woman were confronted by another customer over not wearing masks.
"The dispute escalated, leading to the male customer threatening to cause bodily harm to the other male," the statement read.
Police said that the incident continued in the parking lot, where the man threatened the mask-less individuals with a baseball bat.
"The male then struck the taillight of the victim’s vehicle, causing damage," SSPS added.
A 56-year-old man faces a number of charges, including three counts of uttering threats of death or bodily harm.