The bomber drove into the one-storey building at high speed, collapsing its front part and burying an unspecified number of troops under the rubble, the officials said.
Simultaneously, militants fired rocket-propelled grenades at an army checkpoint near the building.
Militants in Sinai, some with links to al Qaida, have been targeting Egyptian forces for months in the strategic peninsula bordering Gaza and Israel. Their attacks have become much more frequent and deadlier since the removal in July of Egypt's Islamist president Mohammed Mursi.
The Egyptian military earlier this week launched a major offensive against militants in the northern region of Sinai.
Officials have described the offensive, which started on Saturday, as the biggest sweep of the region in recent years, aiming to weed out al Qaida-inspired groups that have taken control of villages in northern Sinai.