A U.N. driver said the blast ripped through the back of the police jeep moments after the column of ten vehicles had left Hagadera, one of three camps in the sprawling complex, wounding two private security guards and two police officers.
Two refugees from the camp were arrested in connection with the attack, police spokesman Eric Kiraithe said in a statement.
Kenya has been plagued by a wave of attacks since it sent hundreds of soldiers into neighbouring Somalia last month to crush the al Qaeda-linked al Shabaab militant group.
“The police car was at the front of the convoy. As we drove out of Hagadera we saw an explosion at the rear end of the landcruiser,” said the driver who declined to be named.
“My car was third in the convoy,” he said.
Abukar Mohamed, a local bus driver, said the blast took place a few hundred metres from the bus park where he was at the time, and sent people scrambling for shelter.
“I then ran to the site of the blast. The two G4S security guards were seriously wounded, they were bleeding all over. The two policemen had minor injuries,” he said.
Witnesses said the attack left a two-metre crater in the sand track.
Dadaab, located about 100 km (60 miles) from the Somali border, was set up in 1991 to house Somalis fleeing violence in their country. The camp’s population has swollen to more than 460,000 people this year because of famine in the lawless country.