The troops said they had been ordered to move out of their barracks in the northeastern city of Maiduguri towards the Gwoza area of Borno state, where the insurgents have reportedly seized pockets of territory.
But one of the soldiers, who asked not to be named, said: "We have vowed not to move one inch until our superiors provide us with all necessary weapons to effective confront and dislodge Boko Haram who have far better arms."
"We are being killed like chickens by Boko Haram because we are not given the required weapons to fight," said another soldier who also requested anonymity. "We say enough is enough."
Some officials and independent experts have said that Boko Haram fighters are better armed than Nigerian troops.
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Borno's Governor Kashim Shettima was fiercely criticised by the military after he made such a claim in February.
Residents in towns raided by the Islamists have said the insurgents are often armed with rocket-propelled grenades and anti-aircraft weapons mounted on trucks and, in some cases, armoured personnel carriers.
Last month, military wives protested at the gate of a military base in Maiduguri trying to stop their husbands from deploying to Gwoza until they were properly equipped.
One of the mutineers said the group was compelled to revolt following an operation to retake the town of Damboa, which Boko Haram seized last month.