Two other troops were seriously wounded in the explosion in Dikwa, a town in Borno State that was recaptured from the jihadist group in July, army spokesman Sani Usman said in a statement.
"The bodies of the two gallant soldiers have been evacuated, to the rear, while the other two wounded soldiers have also been evacuated and are receiving treatment at the military hospital," he said.
The unit also lost an armoured personnel carrier in the blast, he added.
Nigeria's army said in July it had liberated 30 hostages held by Boko Haram, including 21 children and seven women, amid ongoing offensives against the extremists in the Dikwa area.
The town is located around 90 kilometres (56 miles) east of Borno state capital Maiduguri.
Boko Haram has stepped up its attacks since Nigeria's new President Muhammadu Buhari was sworn in on May 29.
The wave of violence since the inauguration has claimed more than 1,000 lives, dealing a setback to a four-country offensive launched in February that had chalked up a number of victories against the jihadists.
Military officials have said it will be more effective than the current alliance in the battle to end Boko Haram's six-year insurgency, which has claimed at least 15,000 lives.
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