Earlier, officials labelled it a "terror" attack which took place at a popular attraction, an ancient Roman amphitheatre, sometime around midday.
But later, Jordanian officials said an investigation into the attack found that the assailant acted alone and had no support from "terrorist" groups.
Two British women, a Dutch man and two female tourists from Australia and New Zealand were wounded in the attack that killed a fellow British holidaymaker.
The Prime Minister Maaruf Bakhit, told journalists that a suspect had been arrested and the gunman has a "police record" but did not elaborate.
A man identified as Nabil Ahmad Issa Jaaoura was taken into police custody and officials said he is a Jordanian of Palestinian origin from Zarqa.
Zarqa, an impoverished town northeast of Amman, is also said to be the hometown of slain Al-Qaeda in Iraq operative Abu Musab al-Zarqawi.
"The result of the primary investigation is that this was a lone act. He does not have any connections with terrorist organisations," government spokesman Nasser Jawdeh later told AFP.
"(Jaaoura) had no ties to any armed group or any suspicious group inside or outside Jordan," he said in an statement carried on state-run Petra news agency. "This is reassurring."
An Iraqi who witnessed the shooting says he saw a man pull out a pistol from his pocket and start shouting “Allahu Akbar” or “God is greatest”, as he fired repeatedly at the tourists.
The shooting spree is the first bloody incident to hit the pro-Western kingdom since November when triple suicide bombings claimed by al-Qaeda killed 60 people at luxury hotels.
Australian shot
An Australian woman caught up in a shooting spree in Jordan has spoken of the horror of watching a friend from her tour group die.
The woman, named by the Nine Network as 22-year-old Ashleigh Blair of Victoria, was shot through the hip.
She said that the bullet passed through a bag she was holding over her shoulder.
Ms Blair said her tour group was preparing to leave the tourist site when the gunman opened fire.
Speaking from her hospital bed she's told ABC radio she thought it was firecrackers and even when she turned to see a guy shooting at them she thought it was a joke.
She said her injured English friend was just pale to begin with then he was just white.
A NSW woman was also caught up in the shooting but was unhurt.
Foreign Affairs in Canberra says embassy officials are helping both women.
'Terror act'
Asked if the shooting was a terrorist act, Foreign Minister Alexander Downer said "it may have been".
He said the Middle East was a place where all Australians should take care.
"Generally, my advice to people is ... particularly your own children, your loved ones who you think so passionately about them, you'd advise them to keep to places which are safe," Mr Downer told ABC Radio.
But it was not necessary to immediately update the Foreign Affairs' travel advice for Jordan, he said.
"I don't know about updating it. The travel advice warns against possible terrorist attacks. We make it perfectly clear (that) in countries like Jordan there are very high risks of terrorist attacks, of course there are," Mr Downer said.
New Zealand Prime Minister Helen Clark said the injured New Zealand woman had undergone surgery at a hospital in Amman and had been able to talk to her family.
Investigation begins
Jordanian Interior Minister Eid Fayez said Jaaoura apparently acted alone but "was determined to kill" as he shot his victims in the back while they were climbing the steps of the Roman amphitheater.
"What happened this morning is a criminal, cowardly and treacherous act. It is a terrorist act that has nothing to do with Jordanian culture or Arab culture," Mr Fayez said.
The interior minister said Jordan would not raise the current level of security that has been in place since the November hotel bombings in Amman.
He was also quick to reassure visitors had nothing to fear.
"Security measures were in place in the area because it is a tourist area ... and we have no plans to take any other measures," he said.
Jordanian officials are investigating the gunman's motives, said Mr Fayez.
A statement from the Jordanian interior ministry identified the victim as Briton Christopher Stocks, according to an Arabic transliteration of the name carried by the state-run Petra news agency.
The British embassy declined to identity the victim before informing his family.
The Dutch tourist was in surgery but his condition was listed as stable, his embassy said.