Police said the suspect, identified as Radcliffe Haughton, 45, was later found dead at the scene with a self-inflicted gunshot wound.
A large number of police had arrived at the Azana spa after witnesses said they saw a man with a gun.
Reports say the incident stemmed from a domestic dispute. The shooting began around 11:15 (15:15 GMT).
Several areas near the spa – including a shopping centre, a country club and a hospital – were locked down, as police searched for the suspect.
A quick reaction Swat team and hostage negotiators were sent to the scene – in addition to FBI personnel.
At least 20 fire, ambulance and police vehicles were also deployed, in addition to a medical helicopter on the ground.
Police initially said they had discovered an “improvised explosive device”, but later said that was not the case.
The White House issued a statement saying Barack and Michelle Obama’s thoughts and prayers were with the victims of “this horrible shooting” and their families.