Nigerian Army spokesman Colonel Sani Usman said the attack happened at about 5:15 am (0415 GMT) in the town of Damboa, some 90 kilometres (56 miles) southwest of the Borno state capital, Maiduguri.
He blamed the attack on "two Boko Haram terrorists".
"The first suicide bomber targeted Damboa Central Mosque but due to stringent security measures he could not gain entry. Obviously frustrated, he exploded and died near the central mosque," he added.
The wounded have been evacuated to a hospital while efforts are on to clear the rubble. Troops and other security agencies have been mobilised to the area."
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The attack is the latest against a mosque in northeast Nigeria and the wider Lake Chad region, as part of a campaign of violence by the Islamist group against civilian "soft" targets.
On June 27, two would-be suicide bombers were killed in Maiduguri, as they tried to target an overnight Ramadan vigil at a mosque on the Damboa Road.
On July 4, the Nigerian Army said it thwarted an attempted suicide bombing by three women against people displaced by Boko Haram in Monguno, northeast of Maiduguri.
There has been a relative lull in attacks, as troops regain control of territory once held by Boko Haram, whose fighters have been pushed into remote rural areas towards Lake Chad.