The shooting spree in Karak, home to one of the region's biggest Crusader castles, is another blow to tourism in a country already grappling with the spillover of the wars in neighbouring Syria and Iraq.
Another 34 people including a second Canadian were wounded in Sunday's assault in the city around 120 kilometres (70 miles) south of the capital Amman.
Four gunmen were shot dead by police during the course of a siege lasting several hours.
"The four dead militants are Jordanian members of a terrorist cell suspected of belonging to IS," a security source told AFP.
Interior Minister Salama Hammad told reporters there was no information about any militants still at large and there had been no arrests. He refused to give the nationality of the gunmen.
Prime Minister Hani al-Malki, who was addressing parliament at the time of the shootings, had spoken of as many as 10 gunmen.
Jordan is a leading member of the US-led coalition fighting IS jihadists in Iraq and Syria.
It has carried out air strikes targeting IS, and also hosts coalition troops on its territory.
Maaz al-Kassasbeh, a Jordanian fighter pilot, was captured by the jihadists when his plane went down in Syria in December 2014, and he was later burned alive in a cage.
Karak is Kassasbeh's hometown.
In June, a suicide bombing claimed by IS killed seven border guards near the Syrian frontier.
According to sources close to Islamists, almost 4,000 Jordanians have joined jihadist groups in Iraq and Syria, and an estimated 420 have been killed since 2011.
King Abdullah II said in a statement Jordan would stand up "to anyone who tries to attack or violate the security and safety of its citizens".
"Jordan is strong and able to stamp out terrorism and its criminal gangs," he said.
But Mohammed Abu Rumman, of the Centre of Strategic Studies at the University of Jordan, was less optimistic.
"No security measures can take on this kind of terrorism without heavy losses," he said.
"A year ago we were talking about a current of sympathy in Jordan for the jihadists."
But "today that current has turned into groups of youth who feel they're an integral part of Daesh", Abu Rumman said, using an Arabic acronym for IS.
Jordan has struggled to revive a tourism sector dampened by the 2011 uprisings across the Arab world, as well as conflict in Iraq and Syria.
The Karak citadel, described by Jordan's Tourism Board as a "maze of stone-vaulted halls and endless passageways", dates back to the 12th century and has withstood many sieges.
Shaher Hamdan, the head of Jordan's association for tourist and travel agencies, said Sunday's attack "will certainly have negative consequences" on tourism.
Jordan's tourism sector "is already affected by any event in the world or in the region, so imagine a terrorist event inside the country", he said.
Tourism accounts for 14 percent of Jordan's gross domestic product (GDP) and is its second highest source of foreign exchange earnings after remittances.
Revenues from the sector dropped from more than $4 billion in October 2015 to $3.1 billion in the same month this year.