Jordan officers killed in attack at Baqaa camp near Amman
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They described the incident as a "terrorist attack".
At least three of the five people killed were intelligence officers, the officials said.
The attack took place at the sprawling Baqaa camp north of Amman at about 07:00 local time (04:00 GMT).
The Baqaa camp was one of six set up in 1968 for Palestinian refugees fleeing the West Bank and Gaza Strip as a result of the 1967 Arab-Israeli war.
Jordan is a key member of the US-led coalition fighting so-called Islamic State in neighbouring Syria and Iraq.
No-one has yet said they carried out the attack.