The gunman used a shotgun in the attack at Kellum Law Firm, which occurred just before noon, and the Walmart across the street from the law office, The (Greenville) Daily Reflector reported.
Greenville Police Chief Hassan Aden said officers shot the man near the entrance to the store.
The names and conditions of the victims and the shooter were not reported.
A spokeswoman for Walmart said no one was shot inside the store, and the store remained open for business, the newspaper reported.
Notable deaths of 2014 [PHOTOS]