The exact breakdown of identities of those killed was not immediately clear. Security and medical sources said at least 70 people, including soldiers and civilians, were killed.
The sources said 38 militants were also killed. The army has acknowledged deaths among soldiers and militants.
Security sources said militants had surrounded a police station in Sheikh Zuweid and had planted bombs around it to prevent forces from leaving.
The militants also planted bombs along a road between Sheikh Zuweid and al-Zuhour army camp to prevent the movement of any army supplies or reinforcements. They also seized two armoured vehicles, weapons and ammunition, the sources said.
"We are not allowed to leave our homes. Clashes are ongoing. A short while ago I saw five Landcruisers with masked gunmen waving black flags," said Suleiman al-Sayed, a 49-year-old Sheikh Zuweid resident.
Ambulance medic Yousef Abdelsalam said he was at the entrance to Sheikh Zuweid but could not enter because of warnings that the road was rigged with bombs.
Witnesses and security sources also reported hearing two explosions in the nearby town of Rafah, which borders Gaza. The sources said all roads leading to Rafah and Sheikh Zuweid were shut down. The interior ministry in the Gaza Strip, run by the Islamist Hamas group, reinforced its forces along the borders with Egypt.
Sinai Province said in Wednesday's statement that it had attacked more than 15 security sites and carried out three suicide bombings.
"It is a sharp reminder that despite the intensive counter terrorism military campaign in the Sinai over the past 6 months, the IS ranks are not decreasing - if anything they are increasing in numbers as well as sophistication, training and daring," Aimen Dean, a former al-Qaida insider who now runs a Gulf-based security consultancy, said in a note.