According to SITE Intelligence Group, which tracks online activity of militants, the IS-affiliated Amaq news agency announced that the group's militants carried out the attack near Saint Catherine.
According to a statement released by the Ministry of Interior (MoI), a crossfire took place between militants and security forces.
After an exchange of gunfire, the attackers fled the scene, the officials said, adding that some of the gunmen were wounded in the shootout.
Egypt's health ministry spokesman Khaled Megahed told Ahram Online the four injured policemen were transferred to Sharm El-Sheikh's worldwide hospital.
At least one policeman was killed and four other were wounded on Tuesday in an attack on a security checkpoint near Egypt's Saint Catherine's Monastery in South Sinai, state television reported. No group claimed responsibility.
Islamic St ate claimed responsibility for the attack on a police checkpoint about 800 meters (yards) from the entrance to the mona st ery, one of the world's mo st important Chri st ian sites.
St Catherine's is one of the world's oldest Christian monasteries and is a Unesco World Heritage Site.
This latest attack is a further blot on President Abdel Fatteh Al Sisi's record, after he pledged to protect minorities in a campaign against extremism.
Egypt has for years been battling an Islamist insurgency in the rugged and thinly populated northern Sinai, which gained pace after the military overthrew President Mohamed Mursi of the Muslim Brotherhood in 2013 following mass protests against his rule.