The attacker also killed a fighter from Haftar’s self-styled Libyan National Army (LNA) when the vehicle they were driving exploded at a roadblock 90 kilometres (56 miles) east of Sirte, General Al-Mabruk Sahban told AFP.
The attack has not yet been claimed.
Sahban added that earlier in the day security services had detonated another car bomb discovered in the area.
The attack on the checkpoint comes a day after Haftar announced the start of an offensive to “liberate” the city of Derna, held by Islamists and jihadists of the Mujahedeen Shura Council.
In March, the Islamic State group claimed responsibility for two attacks against LNA checkpoints that killed 10 people.
Last week, the jihadist group claimed a suicide attack in Tripoli against Libya’s electoral commission that killed 14 people.
Libya has been wracked by chaos since a 2011 uprising that toppled and killed its long-time dictator Moamer Kadhafi, with two rival authorities vying for control.
Haftar supports an administration based in the east of the country. A UN-backed unity government based in the capital has struggled to assert its authority outside the west.