The incident comes a day after a TV journalist survived an attack in Benghazi after coming under a hail of bullets.
Colonel Jelal al-Arafi discovered the device and immediately ran away from the vehicle when the bomb exploded, security spokesman Colonel Abdallah al-Zayedi said.
"He was injured in the foot and underwent surgery at a hospital in Benghazi," Zayedi said, adding that this was an "attempted assassination."
Cradle of the 2011 uprising that ousted long-time dictator Moamer Kadhafi, Benghazi has been rocked by a series of killings of soldiers and police who served under the former regime.
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Yesterday, Khadija al-Ammami, director of Libya Al-Ahrar television's Benghazi office, was shot at several times when she was in her car on the way to her office but miraculously survived, a colleague said.
She later received telephone threats that she would be killed next time.
That attack came three days after a Libyan doctor who hosted a television programme on human development was shot dead by unknown gunmen in Benghazi, Libya's second city.
Azzedine Koussad, a presenter for Libya Al-Hurra television, was hit by several rounds as he sat in his parked car.