The blast happened Sunday afternoon at a rally at Victory Monument in northeast Bangkok, the Thai news agency MCOT reported.
Thavorn Senniam, of the People's Democratic Committee Reform, which led the protest, said he may have been the target of the attack and he had been warned of a possible attack by a high-ranking police officer, the news agency said.
Witnesses said there were at least six people involved in the attack.
A grenade blast during a protest in Bangkok Friday killed one person and injured 39 others, the Wall Street Journal reported.
Police said they were looking for two suspects in the Friday bombing, which opposition leaders blamed on Prime Minister Yingluck Shinawatra's administration. Others have accused protesters of staging the bombing.
In the recent rounds of demonstrations that began Jan. 13 protesters have demanded that Yingluck resign from office ahead of scheduled elections on Feb. 2.
Yingluck, meanwhile, has said the elections will take place, despite the Thai Election Commission's fears the vote might trigger more violence, the Wall Street Journal said.