The attacker detonated his bomb in Spinwam village of the tribal district when he was intercepted on the approach to a checkpoint, officials said.
Pakistan Army have used jet fighters, tanks and artillery in the offensive, which began over a week ago, killing around 300 people they have described as militants, though the number and identity of the victims are impossible to verify.
"At least two soldiers and a civilian have embraced martyrdom," a security official told AFP.
A military statement said that troops stopped the car suicide bomber 100 metres away from a checkpost near a hospital and the action averted major casualties.
The Ansarul Mujahideen militant group claimed responsibility, with spokesman Abu Baseer saying it was the start of a counter-offensive against the armed forces by the Taliban.
"It is beginning of our offensive and we will launch attacks against government and local tribesmen if they form anti-Taliban force," Baseer told AFP via telephone from an unknown location.
Meanwhile, jets and helicopter gunships targeted militant hideouts at several places in North Waziristan, officials said.
The offensive has seen North Waziristan hit by more than a week of shelling and air raids, and more than 470,000 people have fled ahead of an impending ground assault, with many going to the nearby town of Bannu.
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They died today for the tomorrow of your country . Salute their supreem sacrifice .
may the soul of great ones (my beloved soldiers) rest in peace.