It was the third time since August 2009 that Unamid has been the target of an abduction in the volatile region of Darfur.
In April, four South African peacekeepers were seized after two other members of the mission had been taken in August last year. All of them were freed unharmed.
'Targets of violence'
The UN-AU mission is investigating Saturday's incident, along with local Sudanese authorities, but officials said they were unable to say what was the likely motivation for the abduction.
"We don't know why they were abducted," Chris Cycmanick, a Unamid spokesman, told the AFP news agency. "Two other policemen witnessed the incident," he said.
"A trend of abductions of humanitarian workers which started last year is particularly alarming"
UN undersecretary general for humanitarian affairs
At least 19 foreigners have been abducted in Darfur since March 2009. All have since been freed, except an American aid worker with the Samaritan's Purse group who was abducted in May, whose captors are demanding a ransom.
"Humanitarian personnel and assets in Darfur also continue to be regular targets of violence," John Holmes, the UN's undersecretary general for humanitarian affairs, said on Saturday.
"A trend of abductions of humanitarian workers which started last year is particularly alarming."
The abductions place increased pressure on the peacekeeping and humanitarian operation in the region, which has been gripped by a conflict that the UN estimates has left 300,000 dead and 2.7 million displaced.
The UN-AU force, along with international aid agencies, was recently warned by Omar al-Bashir, Sudan's president,that it could be thrown oput of the country if did not respect local authorities.
Khartoum wants Unamid to hand over five men and a woman from a camp for displaced Darfuris in Kalma who had sought the force's protection after clashes between the rebel Sudan Liberation Army and supporters of Qatari-hosted peace talks between rebels and the government.
Sudanese authorities have since blocked five international non-governmental organisations and UN agencies from reaching Kalma, one of the world's largest displaced persons camps during the dispute.