A group of unidentified gunmen opened fire on troops guarding the club, killing one, a security source told Anadolu Agency.
No group has claimed responsibility for the attack.
The Sinai Peninsula, situated near Egypt's borders with Israel and the Palestinian Gaza Strip, has seen almost daily attacks by unknown assailants since the army's July 3 ouster of Mohamed Morsi, the country's first democratically elected president.
Monday's attack brought to 43 the total number of people – including civilians and security personnel – killed in separate militant attacks throughout Sinai since July 5, according to a tally compiled by AA.