The four, who work with the Norwegian Refugee Council (NRC), come from Canada, Norway, Pakistan and the Philippines, regional police official Philip Ndolo told AFP.
"Four foreign aid workers were kidnapped... their Kenyan driver died later while receiving treatment at a local hospital," Ndolo said, clarifying earlier reports that he had also been kidnapped.
Military helicopters and police chased the gunmen, who drove off with the hostages in their vehicle. It was later found abandoned, with fears the gang are heading towards Somalia, some 100 kilometres (60 miles) from Dadaab.
"We have dispatched military helicopters to pursue the kidnappers," Kenyan army spokesman Cyrus Oguna told AFP.
"The vehicle was found abandoned 30 kilometres (18 miles) from Daadab, and we believe the party is still within Kenyan borders, and the captives and their kidnappers are on foot," he added.
NRC is working to support some 465,000 inhabitants in the Dadaab complex, which constitutes Kenya's third-biggest town in size of population.
"A convoy from the Norwegian Refugee Council was involved in an incident in the refugee camp Dadaab," the NRC said in a statement, adding that its head Elisabeth Rasmusson had been travelling with the convoy but was unhurt and safe.
Medical officials with the German government aid agency GIZ said two other people were wounded in the attack, which took place in the sprawling Ifo 2 camp around midday.
The kidnapping is the latest in a series of attacks in the giant Dadaab complex, where gunmen last October seized two Spaniards working for Medecins sans Frontieres (Doctors Without Borders), Montserrat Serra and Blanca Thiebaut.
They are still being held hostage in Somalia.
The kidnapping of the Spaniards was one of the incidents that spurred Kenya to send troops and tanks into Somalia to fight the Al-Qaeda-linked Al-Shabaab insurgents Nairobi blames for abductions as well as for cross-border raids.
Al-Shabaab still control large parts of southern Somalia, despite recent losses to African Union troops, government forces and Ethiopian soldiers, who have wrested several key bases from the insurgents.
Kenya, which invaded southern Somalia in October before joining the AU force, has a heavy troop presence some 120 kilometres into Somalia from their frontier.
Since the 1991 ouster of then president Mohamed Siad Barre, Somalia has been variously governed by ruthless warlords and militia groups, each controlling their own limited fiefdoms.
Hundreds of thousands of Somalis have fled their lawless nation to neighbouring nations since the collapse of a formal government two decades ago, while crippling drought racked the region last year.