According to an eyewitness, the suicide bomber rammed a car into a military vehicle that was part of a convoy.
The attacker’s vehicle was being chased by troops when the bomb went off, a police spokesman said. No group has said it carried out the bombing.
Damaturu is the capital of Yobe state, which has been the scene of frequent attacks by Islamist sect Boko Haram.
State police chief Patrick Egbuniwe confirmed to the BBC that soldiers were among the casualties of Sunday’s attack, but could not confirm whether anyone had been killed.
Some reports speak of up to five dead.
Damaturu is 130km (80 miles) west of Maiduguri, the Boko Haram stronghold.
The group wants Islamic law, or Sharia, to be imposed across Nigeria – and has carried out a series of deadly attacks in the past two years.
Boko Haram means “Western education is forbidden”.
Sunday’s blast follows a failed attempt to blow up the state’s most senior Muslim cleric, the emir of Fika, on Friday.
The bomber tried to drive a car into the emir’s convoy just after he had left Friday prayers. He missed his target but several people in the area were badly injured.