"Police have determined four people are deceased at three locations within a 5 km (3.1 mile) radius," the statement said, Reuters reported.
"A man matching the suspect's description turned himself into the Penticton RCMP detachment. The man remains in custody while the investigation progresses. Preliminary indications are this was a targeted incident," the statement said.
The initial shooting incident was reported at 10:30 a.m. local time (1730 GMT). As police were en route to the scene, a second shooting was reported.
The suspect in both shootings turned himself in about an hour after the first report, police said.
A motive for the shootings was still unknown.
"Determining why this occurred is part of our ongoing investigation," said RCMP regional commander Ted De Jager.
"I understand that this is a deeply troubling incident that has taken place in our community. Our hearts and thoughts are with all those impacted by this terribly tragic incident," he added.