Friday's attack during a funeral at a Greek Orthodox church in the village of Hamoud in Karak governorate, about 120km southwest of the capital Amman, also wounded 40 others.
Witnesses said the shooting lasted several minutes.
Jordan's Public Security Directorate said the men were found while hiding in an abandoned house in Karak.
They refused to surrender and attacked security forces, who returned fire and arrested all three after wounding them, the directorate said in a statement published on state media.
No security personnel were injured, and a number of firearms and ammunition were found in the suspects' possession.
Jordanian authorities have said the violence was carried out by "extremist terrorists".
There has been no claim of responsibility.
"Terrorism has no place among us," the directorate said on Monday, adding that the suspects had met their "just fate".
King Abdullah, a US partner in the fight against Islamist militant groups, has ordered security forces to respond with an "iron fist" to the rare attack on the Christian minority.
Such violence is highly unusual in Jordan, a relatively stable state in the Middle East, though authorities say they have foiled several Islamist militant plots over the years.
Funeral services for the nine slain victims were held on Sunday.
Eight of the coffins were wrapped in Jordanian flags before they were buried in a graveyard in Hamoud.
The Public Security Directorate did not name the suspects or publicly identify possible affiliations with any Islamist militant groups.
Interior Minister Mazen al-Faraya said authorities were reviewing the circumstances that led young people towards extremism and would hold accountable anyone found to have taken part in the attack.
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