The attacks, in an area hard hit by the Boko Haram insurgency, came just days before Nigeria's new President Muhammadu Buhari is to meet his US counterpart Barack Obama.
Buhari is expected to push at Monday's meeting for US help to tackle the Islamist violence, which has surged since he took office in May.
Residents said twin explosions near a prayer ground in Damaturu had killed two people, before a third blast went off moments later near a mosque leaving another 11 people dead, according to medics.
This year's Ramadan has been particularly deadly, with suicide bombers hitting mosques and worshippers attacked by gunmen as they prayed.
"There were two blasts near the Eid prayer ground," said Ahmad Adamu, a security volunteer in Damaturu said of Friday's attacks.
"The first blast went off around 7:15 am (0615 GMT) while security volunteers who had come earlier than worshippers were waiting for the worshippers so they could assist in crowd control. Two were killed and three were injured," he said.
A medical source who wished to remain anonymous told AFP that 13 bodies had been brought to the hospital.
Damaturu is the capital of Yobe, one of three northeastern states hit hardest by the insurgency that has left 15,000 people dead and 1.5 million homeless since 2009.
Nigeria's new army chief Major General Tukur Buratai was due to visit Damaturu on Friday to celebrate Eid with soldiers battling the jihadists, who have pledged allegiance to the Islamic State group that has seized swathes of Iraq and Syria.
Top of the agenda in the talks with Obama "will be measures to strengthen and intensify bilateral and international cooperation against terrorism in Nigeria and west Africa", a statement from the Nigerian presidency said.
Relations dipped late last year under the regime of former Nigerian president Goodluck Jonathan, after Abuja considered US aid to fight Boko Haram insufficient.
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