The explosion was targeted at a Joint Task Force (JFT) patrol vehicle, stationed at Gamboru Market, Maiduguri the state capital.
One of the soldiers was wounded in the attack.
According to the JFT spokesman, Lieutenant Colonel Sagir Musa, the explosive contained acid and highly flammable substances.
Musa also confirmed the that there was no civilian casualty during the attack.
No one has claimed responsibility for the attack but Musa, in a telephone interview with Channels Television, said it has the imprimatur of the dreaded Islamic sect, Boko Haram.