The shootings took place in Karak, a city and tourist destination known for one of the biggest Crusader castles in the region, around 120 kilometres south of the capital Amman.
"Four of the dead are policemen and one is a (female) Canadian tourist," said the source who declined to be identified.
He said nine others were wounded when "unknown gunmen attacked a police station and some patrols in Karak".
Police were hunting the gunmen who fled to the Crusader castle, and authorities have sent in reinforcements, he added.