Anti-Austerity Alliance TD Paul Murphy has called for the perpetrator to be brought to justice and asked anyone who has any information regarding his identity to contact gardai.
Tanaiste Joan Burton was trapped in her car for two-and-a-half hours by protesters in Jobstown in West Dublin last Saturday.
Ms Burton had been attending a graduation ceremony for students at further education centre An Cosan when protesters prevented her car from leaving.
She was also hit with a water balloon, while An Cosan chief executive Liz Waters revealed she was spat at and had her necklace broken.
Mr Murphy, who led the protest, claimed that the incident involving the brick took place after the protest had disbanded and he was no longer at the scene. It is also understood Ms Burton had left the area at the time.
Last night he called for the man who threw the brick to be prosecuted.
"I think he should be brought to justice," Mr Murphy told the Herald. "People should come forward with any information that they have."
Two young men, a 17 and an 18-year-old, were arrested following the protest for public order offences.
However, the man who threw the brick at the garda car was not arrested and is still at large.
Sinn Fein deputy leader Mary Lou McDonald condemned the behaviour of some people following the protest and asked that they stay away from future events.
Speaking about the planned protest outside the Dail on December 10, which is expected to attract people from all over the country, she said: "It must be absolutely peaceful. It should be colourful. It should be determined, but at all times peaceful.
"Hundreds of thousands of people took part in protests organised through October and November and (there were) no arrests.
"To the small number of people who are out there, if they have any ear for what I have to say, this is a peaceful, people's campaign.
"If you cannot be peaceful, if you cannot respect that, stay away."
Taoiseach Enda Kelly told the Dail yesterday that protesters had "descended on the Tanaiste's car like hounds after a fox".
He asked Mr Murphy to apologise for the actions of some protesters, saying: "Deputy Murphy, you should have the courage and the gumption to apologise unreservedly to an Tanaiste for what you caused over the weekend out in Jobstown."
However, Mr Murphy refused.
"I'm not in favour of detaining people or keeping people locked in for very, very long periods of time," Mr Murphy (inset) said last night.
"But I don't think the Tanaiste being prevented from going about her work for two-and-a-half hours is some massive threat to our democratic system, which is what is being portrayed.
"I did argue for the protest to finish earlier than it did. I don't think two-and-a-half hours is a major problem.
"It wouldn't be appropriate to keep someone for six hours or for 12 hours in all likelihood."
Mr Murphy also distanced himself from the brick-throwing incident, saying he did not take any responsibility for it.
"It's not just that I left. It's that Joan Burton left and the protest had finished. The brick being thrown is nothing to do with the protest, as far as I'm concerned.
"I don't regret anything that I did. I regret that certain things happened in Jobstown on Saturday.
"I regret the fact that a brick was thrown at a garda car. But I don't consider that was anything to do with me or my responsibility. I won't be apologising. I have nothing to apologise for."
The Government will announce details of the revised plan on water charges, how they are collected and how to deal with arrears later today.