Officials said the man's life was not believed to be in danger
It went off under the vehicle in the city's La Pena area near the historic centre at about 1325 (1135 GMT).
There was no immediate claim of responsibility for the attack.
It comes days after suspected leaders of the banned separatist party Batasuna were arrested - an action the party described as a "declaration of war"
Spanish media say the injured man is a bodyguard for a town councillor from Spain's ruling Socialist Party, who is believed to be unhurt.
The bodyguard received burn injuries but his life is not thought to be in danger, Basque Country regional government spokeswoman Miren Azkarate said.
"He would have burns on his scalp, on his hands and some superficial wounds on his back," she added.
The politician he had been assigned to protect, Jose Carlos Domingo, told Spanish radio that he and his family had been "really shaken up" by the attack.
Crackdown
While there was no immediate claim of responsibility, Basque regional government sources said the attack bore the hallmarks of an attack by the armed separatist group Eta.
Eta, whose decades-long campaign has led to more than 800 deaths, called off a 15-month ceasefire in June.
The most senior Batasuna official still at liberty, Pernando Barrena, warned of a "new cycle of violence" in Spain following the arrests last week.
Police had detained 22 people in the town of Segura, on the orders of top anti-terrorism judge Baltasar Garzon.
It is believed that Batasuna leaders were meeting there to transfer control to new party leaders.
Mr Garzon led moves to outlaw Batasuna five years ago, accusing it of being an Eta front.
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A bomb wounded a local politician's bodyguard in the northern city of Bilbao on Tuesday, in an attack a senior Spanish Interior Ministry official blamed on the Basque separatist group ETA.

Spanish media say the injured man is a bodyguard for a town councillor from Spain's ruling Socialist Party, who was taken to hospital with burns to his face, right hand, and shoulder.  While there was no immediate claim of responsibility, Basque regional government sources said the attack bore the hallmarks of an attack by the armed separatist group ETA.

It comes days after suspected leaders of the separatist party Batasuna were arrested, an action the party described as a "declaration of war".