The attackers were driving dozens of four-wheel drive vehicles when they swept into the hunters' camp at dawn on Wednesday, officials said.
They struck near Layyah, 190km (118 miles) from regional capital, Samawa.
A wide-scale search has been launched for the attackers, police say.
The Qatari foreign ministry released a statement saying it was working with the Iraqi government "at the highest security and political levels... to find out the details of the Qatari citizens' abduction and work on their release as soon as possible".
It said they had been hunting with official Iraqi permission - though Iraq's interior ministry accused the hunters of failing to abide by its instructions to remain inside secured areas.
The aim of the abduction was "to achieve political and media goals", the interior ministry said.
The remote area where the incident took place is highly tribal in nature and a Shia region, reports the BBC's Jim Muir in Beirut.
The Shia political parties which dominate the Iraqi government are highly critical of Qatar's role in supporting Sunni rebels in Syria - so this is bound to be a serious diplomatic incident, he says.
Iraq is one of several countries frequented by Gulf Arab huntsmen and falconers as they search for prey that either does not exist in their own countries or which has been almost hunted to extinction there.
Their favoured prey is the Asian houbara bustard, akin to a small turkey, and to find it and other similar species Gulf hunters often travel to Morocco, Iraq, Pakistan and Afghanistan.
They take with them their prized falcons, typically peregrines, sakers and lanners, which are expertly trained to home in on their quarry at high speed. According to a former CIA officer, in 1998 a CIA-run sniper team in Afghanistan observed Osama Bin Laden and his al-Qaeda followers gathered at a camp near Kandahar but they were ordered to take no action for risk of harming the Emirati hunters who were with them.
Other Gulf hunting expeditions have even extended as far as the Central African Republic in search of big game.
Two Iraqi officers providing security for the party were also taken by the gunmen but later released, officials said.
No details were provided on which members of the Qatari royal family were among those held.
Wealthy practitioners of the ancient sport of falconry from various Gulf states often travel to the area at this time of year.
The hunters had been escorted by Iraqi security forces but they decided not to engage a large number of gunmen, a police colonel from Samawa - the capital of Muthanna governorate - told Reuters.
"We are talking about at least 100 gunmen armed with light and medium weapons," he said.
More than 12 years after the US-led invasion and occupation, Iraq is still plagued by violent crime and militant attacks.
In September, 16 Turkish construction workers were freed a month after being kidnapped in the capital, Baghdad, apparently by Shia Muslim militants.
Falconry was an important skill for Bedouin hunters in the harsh deserts of Arabia and Syria and has been around for thousands of years.
But the Asian houbara bustard (or MacQueen's bustard) - a likely target of the kidnapped hunters - only came to prominence as a favoured prey in the 1970s, when lavish hunting trips became popular, and when the availability of four-wheel-drives and guns prompted a sudden decline in the species, which is now threatened.
The bird's popularity may be partly explained by its elegant plumage and because some consider its meat to be an aphrodisiac.
Arabs' pursuit of the Asian houbara has caused tension elsewhere. There has been growing hostility in Pakistan, where Gulf Arab hunting parties were until recently regularly granted permission to bring in falcons to hunt the Asian houbara despite a ban on locals hunting - and sometimes killed thousands at a time. Amid a conservationists' outcry, two months ago Pakistan's Supreme Court ordered a total ban on hunting of the species.
Gunmen have kidnapped at least 27 Qatari hunters - including members of the ruling family - in a desert area of Iraq near the Saudi border, say police and the local governor.