The bombing at Phramongkutklao Hospital, which is popular with retired military officers, took place on the third anniversary of a 2014 military coup.
"It was a bomb. We found the pieces that were used to make the bomb," Kamthorn Aucharoen, commander of the police's explosive ordnance team, said.
"Right now, authorities are checking out closed circuit cameras."
The deputy commissioner of the Royal Thai Police said investigators found traces of batteries and wires at the blast site.
It comes just weeks after a double explosion at a shopping centre in Pattani, southern Thailand, injured at least 50 people.
A suspected car bomb was detonated at the entrance to the Big-C shopping centre in downtown Pattani on 9 May, a province that has suffered waves of secessionist violence since 2004.
A first bomb was detonated inside the building, followed by a second explosion outside the centre, which targeted shoppers running from the first blast.
Bangkok bomb: Explosion at hospital in Thailand leaves at least 24 injured
22 May 2017
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Thai police say 24 people have been injured in a bomb explosion at a hospital in Bangkok.
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