A group of anti-globalisation demonstrators on Saturday smashed shop windows, witnesses and police said.
The group of about 50 protesters attacked the offices of a temporary work agency in an area between the city centre and the summit venue before being chased away by police.
An ambulance was seen moving in to take away an injured demonstrator. Witnesses said a petrol bomb was thrown at the work agency office. Smoke could be seen billowing from the agency.
Police said 24 people were taken into custody at police headquarters for questioning.
The protests came as leaders from both the EU's current 15 members and the 10 countries due to join the Union next year opened a summit in the Italian capital.
The demonstrators say the proposed constitution is designed to promote the free market and capitalism and is not focused enough on the need to build peace and understanding.
Special trains had earlier brought in large numbers of demonstrators from all over Italy, including Milan, Palermo and Venice.
Earlier, a crowd of around 500 anti-globalisation protesters gathered outside the main government offices in central Rome and threw toilet rolls at the building while shouting insults.
Police used batons to control the crowds, but made no arrests, officials said.
On Friday, a small group of demonstrators dumped several buckets of manure in front of Prime Minister Silvio Berlusconi's private residence in Central Rome.
Unionists join protests
In unison with the anti-globalisation march later on Saturday, thousands of trade unionists are scheduled to parade through the centre of Rome to protest against not only the summit, but also the government's labour and pension reforms.
Over the past year, the Italian government has tried to overhaul both the labour and pensions systems, leading to protests by trade unions, which have called a general strike later this month to oppose the pension reforms.
Earlier this week, a letter bomb exploded in the mail room of the Labour Ministry in Rome, causing some damage but no injuries.