A gunman has killed one person and wounded another at a shopping centre in Bangkok, police said, 10 days after a mass shooting at another mall in Thailand's northeast.

The shooting at the Century The Movie Plaza on Tuesday, near the Thai capital's Victory Monument, was a personal issue and the attacker fled the scene, the Thai police said.

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"One person died and another was injured," police Colonel Krissana Pattanacharoen told Reuters news agency.

Police said in a statement they knew the suspect's identity and were working to apprehend him.

Ten days ago, a soldier had killed at least a dozen people at the Terminal 21 shopping centre in the northeastern city of Nakhon Ratchasima.

He had earlier killed his commanding officer, other soldiers at his base and several people at a Buddhist temple.