Mr Martin said the protests posed “an unacceptable risk to both the public and gardaí”.
In a statement, the Taoiseach said: “The large gathering, in the face of ongoing Covid-19 restrictions, showed a complete lack of respect to the people who have made huge sacrifices during this pandemic.
“Nor can we tolerate the thuggish behaviour or attacks on gardai, who have the public’s utmost respect as they continue to protect and serve our society in difficult circumstances.
“There can be no justification for the march or the violence that unfolded, and I pay tribute to members of An Garda Siochana who moved quickly to make arrests and restore order.”
The Minister for Justice has also condemned the violence in Dublin following an anti-lockdown protest.
Helen McEntee described the clashes as “completely unacceptable”.
In a statement Ms McEntee said: “I have spoken to the Garda Commissioner this evening and he has told me the disturbance in Dublin is being brought under control.
“I know there have been a number of arrests already today and a special court sitting is being arranged to make sure these law-breakers are prosecuted speedily. I understand fixed charge notices have also been issued to a number of people.
“I want to commend the courage and professionalism of the Gardai on duty today in Dublin who responded with great control and discipline in an extremely challenging situation.
“This situation was completely unacceptable and was an insult to so many who have worked so hard in the fight against Covid-19 and to those who have died.
“This mindless thuggery showed a wilful and blatant disregard for the public health rules which are needed to help us all and keep us safe.”
Fireworks and other objects were thrown at gardaí during the protest.
Harris condemns “thuggery” as fireworks thrown at…
Tánaiste Leo Varadkar said he was “horrified” to see protesters clash with police on the streets of Dublin.
Mr Varadkar tweeted: “Irish people have spent last year fighting Covid.
“There is no excuse for violence to gardai or anyone.
“This behaviour on Grafton St by a selfish few undermines sacrifices that millions have made in the last 12 months.”