The assailants fired for several minutes in broad daylight during a funeral at a Greek Orthodox church in Karak governorate on Friday, in what Jordanian authorities described as an act of extremist terrorism.
There was no immediate claim of responsibility.
Such attacks are rare in Jordan, although authorities in the US-allied kingdom say they have repeatedly foiled plots by Islamist militants in recent years.
Authorities said they were still searching for the attackers, adding it was too early to determine whether they had links to known groups inside or outside Jordan.
"A massacre, a massacre in every sense of the word," said Tarek Ammarin at a hospital where the wounded were being treated.
A relative of Ammarin's was injured in the attack.
Reuters video footage showed police patrolling on Saturday outside the Hamoud church, about 120km southwest of the capital, Amman.
"This is a result of a terrorist ideology and blind extremism and we will not allow society to go down this path," Prime Minister Jafar Hassan said in a post on X.
Jordan's King Abdullah, a US partner in the fight against militant Islamist groups, visited Karak hours after the attack and said the perpetrators would be punished "with an iron fist".
Christians make up a minority of Jordan's population.
The country is home to several biblical sites that attract Christian pilgrims from around the world.
Jordan has been among the US allies in the Middle East to be hit by Iranian attacks after the US and Israel launched strikes against Iran in February.
