Police officers were called on Sunday to the shooting site at Emerson Food Market in north Minneapolis where they found one man was dead from an apparent gunshot wound, Star Tribune newspaper reported.
One person was arrested in connection with the shooting, the police said.
Local reports said the fatalities brought to five the total number of homicides in Minneapolis over the weekend.
"This weekend has been an anomaly," Minneapolis police spokesman John Elder said, adding that "we look forward to addressing the reasons for this spike in violence".
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