“We killed over 50 of them,” said Lt Gen Ihejirika.
The group, whose name means “Western education is forbidden”, often targets security forces and state institutions.
“They came with sophisticated and heavy weaponry… and bombs but our trained soldiers subdued them,” Lt Gen Ihejirika told local radio.
Deaths were also reported after clashes in Potiskum to the west of Damaturu.
The fighting had erupted in Damaturu – the state capital of Yobe – on Thursday afternoon, Police Commissioner Tanko said earlier.
One eye-witness told the BBC that bomb blasts and shooting could be heard around Damaturu for several hours.
“People are scared and they are just moving out of the town now,” said the witness, who gave his name as Suliman.
Boko Haram first came to prominence in 2009 when hundreds of its followers were killed when they attacked police stations in Maiduguri.
Its founder, Mohammed Yusuf, was arrested but died in police custody.
Boko Haram resumed its attacks – mostly in Maiduguri – a year later and has since staged deadly raids across the mostly Muslim north, as well as central areas such as Jos and Abuja.
Under Yusuf’s leadership, the group demanded that Nigeria become an Islamic state but it is now believed to be made up of several factions, with various demands.