On Monday, Boko Haram set a police base on fire and attacked a university and school.
The state governor’s office stated the move would allow the security forces to finish their operation to drive out the attackers.
A statement issued by an adviser to the Yobe state governor stated the decision to impose a curfew on Tuesday had been "taken… as part of measures to enable the security agents, who did a great job yesterday, repelling insurgent attacks on the town, to conclude their ongoing assignment."
The curfew means that all residents will have to stay at home, forcing the closure of schools, businesses and government offices.
Damaturu has been targeted by Boko Haram a number of times before. At least 63 people were killed in an attack on churches and police in 2011 in what was then the deadliest attack of the insurgency.