The explosion occurred in the Sharqiya province in the Nile Delta and destroyed the front compound wall of the building, the army said in a statement.
The blast comes after Egypt was hit by two attacks in less than a week. On Tuesday, a suicide car bomber killed 15 people at a police building in Mansoura, north of Cairo.
And on Thursday a bomb in Cairo wounded five people on a bus.
The army said today's attack was a "continuation of cowardly terrorist acts".
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But the Brotherhood said in a statement that "it is innocent of any violent incident that has (been) or will be committed".
The designation means hundreds of thousands of members of the Islamist organisation now face prison sentences if they hold demonstrations or are found in possession of Brotherhood recordings or literature.
Since Morsi's ouster by the military on July 3, security forces have launched a crackdown on the group, that has seen more than 1,000 people killed and thousands of the toppled president's backers arrested.