The injured include a second Canadian tourist and 20 Jordanians, police said.
The identity and number of the assailants remain unknown, and no group has yet claimed responsibility. A person close to Jordan's security agencies said authorities believe the assailants were extremists with ties to al-Qaida or the Islamic State.
The US Embassy in Amman issued a statement to citizens warning of an "active shooter" in Karak, 130km south of the capital, and urged citizens to "avoid that area for the time being."
Jordan has long been hailed as an oasis of stability and security in the violence-plagued Middle East, with wars and terrorist havens near its borders with Syria to the north and Iraq to the east.
However, the image of stability is being eroded. Sunday's attack marked the fourth deadly targeting of Jordanian security and army personnel this year.
In March, a cell of Islamist militants linked with the Islamic State engaged in a shootout with police in the northern city of Irbid, leaving one policeman and seven gunmen dead. A gunman killed five General Intelligence Department officers in Baqaa refugee camp, a few miles north of the capital, in June. Later in June, Islamic State militants executed a truck-bombing, killing seven Jordanian soldiers stationed near a makeshift refugee camp along the Jordanian-Syrian border.
In November, a Jordanian officer opened fire and killed three US military trainers at an air base near Jafr used for training Syrian rebels - although the motives behind the shooting are still unclear.
While the Islamic State has not announced a branch in Jordan, the group has a force of 1400 known as the Khalid ibn al-Walid Army a few miles away from the Jordanian-Syrian border near the city of Deraa. Security officials privately say the Islamic State likely has at least a "sleeper cell" in the country.
Although Jordan is a major ally in the war on the Islamic State, 3,000 Jordanians fight under its banner, experts say, making up one of the largest foreign contingents in the extremist group.
Jordanian officials have repeatedly expressed their concerns of the threats to the kingdom should these fighters return home.