It was earlier reported eight people were hurt.
The Erawan Emergency Centre later announced 20 people were being treated for injuries caused by the Banthat Thong blast, and subsequently raised the figure to 36, one seriously.
The bomb, either an improvised explosive or a giant firecracker, went off as the People's Democratic Reform Committee protesters were passing along the street near Charoen Phol intersection, the Bangkok Post reporter following Mr Suthep said.
The explosion, about 1pm, occurred about 200 metres from where Mr Suthep was standing, the reporter said. Security guards whisked Mr Suthep away to an unknown location.
It was unclear whether the bomb was placed on the roadside and trigged by remote control, or thrown from a building in the area, BlueSky television said.