"A large explosion" targeted the military intelligence headquarters in Rafah on the border with the Gaza Strip, one official said.
Witnesses said the powerful blast shattered the windows of other buildings in the Imam Ali area in Rafah where the military building is located.
Minutes later, a second explosion hit an army checkpoint nearby. There were no immediate reports of casualties.
The attacks come just days after an al Qaeda inspired group in the peninsula claimed credit for a Cairo bombing that targeted the interior minister last week, pledging more attacks.
The military has poured troops and armour into Sinai to crush an insurgency that surged after the army overthrew the president Mohamed Morsi on July 3.
A subsequent crackdown on insurgeons by authorities left hundreds dead.
In its statement, the Ansar Beit al-Maqdis group - Partisans of Jerusalem in English - had blamed interior minister Mohammed Ibrahim and army chief Abdel Fattah al-Sisi for the killings of hundreds of Morsi's supporters.
"We call on all Muslims in Egypt to stay away from all military and interior ministry installations to preserve their lives," the group said.
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