Thai television showed the protesters hurling rocks, water bottles and other objects.
At least seven protesters were taken to hospital with minor head wounds and other injuries, hospital officials said.
Protests will continue
Jakrapob Penkair, a former Thaksin government spokesman who is now a key leader in the Democratic Alliance Against Dictatorship, said: "The authorities tried to break up our protest without even trying to talk to us."
He vowed the protests would continue.
Some have said the coup stemmed from middle-class street protests in 2006 against Thaksin's autocratic style and huge personal wealth, which his opponents said he used to secure the support of rural voters.
But other analysts say it was as much about a royalist military and corporate elite removing a moneyed, ethnic Chinese businessman who had encroached too far on their traditional turf.
Thaksin was in New York at the time of the coup and has spent most of his time since he was toppled from power in London, where he is buying English football club Manchester City.
He has also travelled round Asia playing golf and giving interviews and lectures that have unnerved the coup leaders.
Last week, Thaksin sued a military-appointed anti-corruption panel for $1.5bn in compensation for damage caused by its order to freeze $1.58bn of his assets.