The attackers took dozens of people hostage, with security forces in Mali saying that 20 had been freed. It was unclear how many remained in captivity.
The Government of Mali says that "suspected jihadists" are carrying out the attack.
"There is an attack by presumed jihadists on the Kangaba camp," one official told AFP.
An MFat spokesman said it was following up on reports of the attack in Mali.
"There are no indications at this stage that any New Zealanders have been caught up in the attacks at Le Campement resort in Dougourakoro.
"There are currently two New Zealanders registered as being in Mali. The ministry has had no requests for consular assistance."
Modibo Traore, a spokesman for the Malian special forces in the former French colony, said there were three or four attackers.
The resort, popular with expats on the weekend, features a hotel and restaurant with three small swimming pools. Bicycles and kayaks can be rented, and the site includes football and volleyball pitches.
A UN official said those at the resort when the attack began included people affiliated with the French military mission, as well as the UN. Mali is currently home to 1600 French soldiers, stationed in the north of the country on the largest French military base outside of France.
"I heard gunfire coming from the camp and I saw people running out of the tourist site," said Modibo Diarra, who lives nearby.
"I learned that it was a terrorist attack."
Over an hour after the first reports of the incident, helicopters hovered over the site and a large black plume of smoke billowed into the sky.
Last week the US State Department updated its travel advice to warn its citizens of an increased threat of attack in Bamako.
"The US Embassy informs US citizens of a possible increased threat of attacks against Western diplomatic missions, places of worship, and other locations in Bamako where Westerners frequent," it said on June 9.
Americans, currently advised to avoid all travel to Mali, were told: "Avoid vulnerable locations with poor security measures in place, including hotels, restaurants, and churches."
A state department spokesman told the Telegraph that they could not say whether the updated advice was in relation to any specific threat.
The Foreign Office, unlike the state department, does not advise against all travel to the country - instead issuing the milder advice that Britons should avoid "all but essential travel" to the African nation.
Britons are, however, told not to go at all to the areas of Timbuktu, Kidal, Gao and Mopti, and parts of other provinces.
"Terrorists are very likely to try to carry out attacks in Mali, including kidnaps," the Foreign Office said in its advice, updated on Saturday.
"Attacks could be indiscriminate, including in places visited by foreigners."
A Foreign Office spokesman told the Telegraph they were monitoring the situation closely.
Emmanuel Macron, the French president, visited the northern city of Gao last month, at the end of his first week in office, to discuss fighting terrorism with his Malian counterpart, Ibrahim Boubacar Keita.
France intervened in its former colony in January 2013 to drive out al Qaeda-linked groups that hijacked a rebellion in 2012 by ethnic Tuaregs, and attempted to take control of the central government in Bamako.
In November 2015 Islamist militants took 170 hostages and killed 20 of them in a mass shooting at the Radisson Blu hotel in Bamako.
