The 57-year-old from Dudley was arrested after several people called to report the incident yesterday.
Workers suspected a man was shoplifting and, when confronted, he was reported to have coughed on staff and laughed at them.
High Street-based Black Country T shirts warned neighbouring businesses about the incident on Facebook.
A spokeswoman for West Midlands Police said: "A 57-year-old man was arrested on suspicion of theft and assault earlier this afternoon in Dudley.
"It’s understood he coughed on staff who suspected he was shoplifting, and claimed to be infected with coronavirus.
"He was arrested by officers on Dudley High Street after several people called to report what happened.
"The man, who is from Dudley and has suspected mental health issues, has been taken into custody and will be questioned in due course.
"Those affected have been given appropriate advice and referred to the non-emergency NHS helpline for further support and guidance."