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A doctor at a Bangkok emergency centre said the wounded had been hit by shrapnel.
It was the most serious incident in long-running protests since five people were killed and dozens wounded in clashes on Feb. 18, when police made their most determined effort to clear demonstrators.
Protesters have been on Bangkok's streets since November trying to bring down the government and there have been regular small attacks and clashes.
Twenty-seven people have been killed and hundreds wounded since the protests began, according to police and hospitals.
The protests are the latest phase in nearly 10 years of hostility between the royalist establishment and ousted former Prime Minister Thaksin Shinawatra.
The army has a long record of intervening in politics but military chiefs have stayed aloof from this crisis, insisting that politicians must sort out the dispute.
However, street violence raises the possibility of military intervention aimed at restoring order.