Protesters set alight rubbish bins as riot police charged them in the city centre, near the parliament building.
Seven people were arrested and at least six injured, officials said.
Earlier, tens of thousands of people held largely peaceful protests across Spain against the latest government austerity measures.
Public sector workers crowded the streets of Madrid, Barcelona and several other cities, chanting slogans against government “robbery”.
Among those protesting were firefighters and police officers, as well as health and education workers.
“We have lived through bad times, but this takes the biscuit,” fireman Francisco Vaquero, 58, told the Reuters news agency.
The new 65 billion-euro ($80 billion) package of public sector wage cuts and tax rises were announced last week by Prime Minister Mariano Rajoy.
He said it was part of a deal with eurozone leaders to help rescue Spain’s troubled banks. Parliament ratified the measures on Thursday.
Earlier in the day, Germany’s parliament voted in favor of the 100 billion-euro bailout for Spain’s debt-laden banking sector.
Government austerity measures aimed at cutting Spain’s large deficit have prompted frequent protests, including one by miners against subsidy cuts last week.
At a debt auction on Thursday, Spain managed to raise 2.98 billion euros on the financial markets, but at the cost of sharply higher interest rates compared to an auction last month.
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