The group suffered heavy casualties and six of its bases were destroyed, the military said.
However, Nigeria`s military has said the strikes were not on its territory.
In a statement, it said it had identified the targets but the raids probably hit Niger.
"The territory of Nigeria has not been violated," it said.
Both Chad and Niger have been helping Nigeria fight Boko Haram in recent months.
The BBC`s Nathalie Magnien in N`Djamena says Chad has carried out airstrikes in Nigeria before, when it entered the conflict in January.
However, the strikes are the first since Monday`s twin blasts which killed more than 20 people and wounded more than 100, she adds.
`Merciless`
The attacks on the police headquarters and a police academy in N`Djamena were the first in the city, blamed on Boko Haram.
The group has not commented, but it had previously vowed to attack Chad because of its military support for Nigeria.
Chad will continue its "merciless" pursuit of the militants "so that no drop of Chadian blood spilt goes unpunished," the military said.
It did not mention where the raids took place.
Chad is to host a new regional force being set up to tackle Boko Haram.
It believes the group threatens the stability of the entire region.
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