Here's the deal ... video posted on social media shows 2 black men wearing surgical masks being tailed by a police officer as they head for the exit of the Walmart in Wood River, Ill.

The men claimed the cop told them a city ordinance bars people from wearing masks at businesses. In the video -- which was posted on March 18, but is just now going viral -- the men said they were being forced to leave.

At the time of the incident, Illinois Governor J.B. Pritzker told residents to only wear masks if a health care professional recommended it. The directive broadened at the end of the month, and now other cities are ordering folks to cover their faces in public.

Wood River Police Chief Brad Wells responded Wednesday to growing criticism ... and said the officer was trying to identify the individuals because he felt they were acting suspiciously before entering the store.

The chief admits the officer told the men a city ordinance prohibited the masks -- even though such an ordinance does not exist. He adds, however, there is an Illinois law prohibits wearing a mask to conceal your identity from cops ... without written permission from the property owner.

The police chief says it's understandable why someone would wear a mask to protect themselves in the current pandemic, but he says not many people were wearing masks back when the video was shot -- and claims no one else in the store was doing so.

Wells adds, the men refused to provide ID, and said they were leaving. He claims the men left on their own and were not ordered to leave the store.

According to police, the men in the video have since made a formal complaint and it's under internal investigation. Wells says the NAACP and FBI will also review the incident.