The shootout occurred during a raid on a suspected militant hideout in an abandoned house in al-Arish, MENA said, citing an un-named security source. Three machine guns and a rifle were found at the hideout, MENA said.
The report did not mention any casualties or wounded among the security forces.
Interior ministry officials were not immediately available to comment on the report.
Egypt in February launched a highly-publicized operation against Islamic State militants who have waged years of attacks on security forces and civilians, killing hundreds.
The death of the 11 brings the total of those killed since the beginning of the operation to at least 261 suspected militants, according to a Reuters count based on military statements. At least 35 military personnel have also been killed since February, according to a Reuters count based on military statements.
President Abdel Fattah al-Sisi ordered the armed forces in November to defeat militants within three months after an attack on a mosque in Sinai killed more than 300 people.
Defeating Islamists and restoring security after years of unrest has been a promise of Sisi, who was re-elected in March in a landslide victory against no real opposition.
Sisi’s critics say his presidency has brought a harsh crackdown on dissent, but supporters say such measures are needed to stabilize Egypt, which was rocked by years of unrest after protests toppled veteran leader Hosni Mubarak in 2011.
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