It is the first area to fall under a curfew since a state of emergency was declared in three states.
A BBC reporter in Adamawa says the decision is surprising, as the security situation there is less serious than in Borno and Yobe states.
Boko Haram militants have waged an insurgency in Nigeria since 2009.
More than 2,000 have been killed in the conflict, which has its roots in north-east Nigeria.
Mobile phones down Nigerian military spokesman Brig Gen Chris Olukolade said "every resource available" to the armed forces would be used in the operation against Boko Haram.
BBC Nigeria correspondent Will Ross says this is confirmation that fighter jets and helicopter gunships are likely to be deployed.
When asked whether this would not put civilians in harm's way, Brig Gen Olukolade said the enemy bases to be targeted were in unpopulated areas close to Nigeria's borders.
Our reporter says the hardest part of this campaign will be in urban areas like the Borno state capital, Maiduguri, where the Islamist militants are living among the civilian population.
Mobile phone networks were not functioning in many parts of north-east Nigeria on Thursday, but our reporter says it is not clear if this is related to the current military offensive.
Militants have previously attacked mobile phone masts in the area in an effort to disrupt communications.
The BBC's Abdullahi Tasiu Abubakar reports from Adamawa city that most people he spoke to felt the curfew was unnecessary and it would merely disrupt their lives.
The president said the army would take "all necessary action" to "put an end to the impunity of insurgents and terrorists".
Boko Haram, whose name means "Western education is forbidden" in the local Hausa language, is fighting to overthrow the government and create an Islamic state in the north.
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