It happened at the University Market in the 1100 block of Chapel Hill Street.
Detectives said it appeared there was some kind of argument between the clerk and a customer that led to the gunfire.
The clerk - Alaael Ahmed El Hamalawi, 52, of Durham - was arrested and charged with assault with a deadly weapon inflicting serious injury and discharging a firearm in the city limits. He was released from jail after posting a $75,000 bond.
The man who was shot - John Reid Jr., 55, of Durham - was treated for non-life-threatening injuries. He faces charges of communicating threats and injury to property.