It was the first death in a weeklong series of protests that had been largely peaceful, Voice of America reported.
The leader of the protests, Suthep Thaugsuban, was not injured when the bomb was thrown at the crowd Friday.
Suthep is calling for Prime Minister Yingluck Shinawatra to step down before elections Feb. 2. The opposition has said it will boycott the voting, calling instead for an unelected people's council.
Suthep blamed the government for the bombing, but police said questions had been raised by a last-minute change in the protest route by opposition leaders that took protesters past a building that was being demolished, the Bangkok Post reported.
The bomb was thrown from the building, hitting protesters about 110 yards from Suthep. He was whisked away by guards.
Military police and opposition guards who inspected the building later said an assortment of weapons, including rifles, were found in one room. Suthep later aired a video clip he said showed forged police pass cards and hand-held radios that also were found in the room.
The protests prompted about 1,200 people to donate blood following a plea from the Thai Red Cross. Blood reserves had dropped by half because protests had caused many roads around the National Blood Center to be closed, said center director Dr. Soisaang Phikulsod.
Soisaang said the center had not put out a call for blood out of concern that might be interpreted as an endorsement of violence.