"Investigations are under way but early indications are that this was an isolated and individual act," said government spokesman Mohammed Momani, announcing the arrest without identifying the suspect.
The gunman struck at Baqaa camp north of the capital early on Monday -- the first day of the Muslim holy month of Ramadan -- in what Momani called a "terrorist attack".
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A security source told he was arrested later at a mosque in the Salt region north of Amman.
The suspect was armed and resisted arrest, the source said, adding that a police officer had been injured in the swoop.
No group has claimed responsibility for the attack.
Jordan is a leading member of the US-led coalition fighting the Islamic State group in neighbouring Iraq and Syria, and has been the target of jihadist attacks.
The five agents, who had been starting their shift, were buried later in the day in their home towns, with hundreds of members of the security services in attendance.
Security forces blocked road to the camp, 20 kilometres from central Amman, to keep journalists away, an AFP correspondent said.
The Baqaa camp is the largest of the kingdom's 10 official Palestinian refugee camps.
Home to about 220,000 people, including more than 100,000 of the two million Palestinian refugees who live in Jordan, its residents suffer chronic poverty and unemployment.
It was unclear whether the gunman was a resident of the camp or an outsider, a security source said earlier yesterday, adding that experts were examining CCTV footage for clues.
Jordan has seen spillover from the conflicts in Iraq and Syria in the past.
In December 2005, suicide attacks on three Amman hotels claimed by IS's predecessor, Al-Qaeda in Iraq, killed 60 people and wounded dozens.
Former member of parliament Mahmud al-Kharabsha said what happened at Baqaa had been "expected".
"This camp was chosen for an attack in order to sow sedition (between Palestinians and Jordanians) in the country," Kharabsha said.
"What happened was expected. Jordan is in the midst of a cyclone and shares long borders with Syria and Iraq," he told AFP.
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