"The suicide bomber aged 15 blew himself up" in a busy market area near a police station in the town of Sheikh Zuweid leaving seven dead and 26 wounded, an interior ministry statement said.
A six-year-old child was among the victims, the statement added.
IS, which has waged a bloody insurgency in the region, released a statement on its social media accounts claiming responsibility and praising the suicide bomber.
Egyptian security forces have been targeted by extremist groups since the army overthrew president Mohamed Morsi in 2013.
Egyptian military kills 52 militants in Sinai
Hundreds of soldiers and policemen have been killed in a string of attacks that has also claimed the lives of civilians, particularly among the minority Coptic Christian community.
Egypt in February last year launched a military offensive against IS in the Sinai peninsula.
Around 600 suspected militants and about 40 soldiers have been killed so far, according to official figures.
Tuesday's deadly attack comes days after gunmen opened fire on a police vehicle in Cairo killing a police officer and a civilian driver.
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