The incident occurred in Hartford County early Monday, June 3, in Canton.
Paul Copleman, spokesman for the state Department of Energy and Environmental Protection, said the bear, an adult male, had gotten into the "unsecured" dumpster.
The business owner, who was not named, was cleaning up the mess when the bear returned.
Copleman said wildlife personnel and EnConn police responded to the scene.
He did not release details regarding the shooting of the bear but did confirm the business owner shot and killed the bear as it approached.
"The incident is under investigation at this time," Copleman said.
DEEP says dumpsters should be secured with a reinforced plastic lid and must have a bear-resistant lock bar. Metal clips also help ensure the dumpsters.
Homeowners should also have bear-resistant garbage cans with locking lids.
There is no word on whether the business owner was injured.
This is a developing story. Check back to Daily Voice for updates.
Click here to follow Daily Voice Greenwich and receive free news updates.