Three officers were taken to hospital, police said. There were also reports of injuries among protesters.
The clashes began when police charged at masked protesters at a "Welcome to hell" march attended by 12,000 people.
World leaders - including US President Donald Trump - will discuss climate change, trade and other major issues.
Police fired water cannon and pepper spray at masked protesters, who hurled bottles, stones and flares.
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Organisers cancelled the march where the first clashes took place, but protesters remained on the streets and police said violence spread to other areas of the city.
Protesters built makeshift barricades, set vehicles alight, damaged businesses and repeatedly shone a laser at a police helicopter to dazzle its pilot, police said.
Medics were seen treating several people. At least one person appeared to have been seriously hurt and was carried away covered by a foil blanket.
Before the march, police had warned of possible violence and said they had confiscated a number of homemade weapons.
Some 20,000 police have been deployed in Hamburg for the summit, and security cordons have been erected to prevent protesters reaching the venues. Up to 100,000 protesters are expected in Hamburg during Friday and Saturday.
G20 discord
The G20 leaders face their own disagreements, including over climate change and trade.
Mr Trump has already met German Chancellor Angela Merkel and the pair spent an hour talking about North Korea, the Middle East, the conflict in eastern Ukraine and G20 issues, a German government spokesman said.
Last week Mrs Merkel said the G20 would focus on the Paris climate deal - which the US has withdrawn from. But earlier she said that as the G20 host she would work to find compromises.
- Putin and Trump in their own words
The summit will also see Mr Trump meet Russian President Vladimir Putin for the first time. The meeting will take place at 14:45 local time (13:45 GMT) and last for an hour, Russian media report.
Russia 'destabilising' Ukraine
Earlier in the day Mr Trump used a speech in the Polish capital Warsaw to call on Russia to stop "destabilising" Ukraine and other countries.
Russia should also end support for "hostile regimes" such as those in Syria and Iran and "join the community of responsible nations", he said.
He urged Russia to join the "fight against common enemies and in defence of civilisation itself".
The Kremlin rejected his comments.
Mr Trump referred to Russia's "destabilising" behaviour twice in one day in Poland. But the Kremlin spokesman has shrugged that off, saying simply that Moscow "does not agree". It's all part of the wait-and-see approach here.
Russia once had great hopes that Donald Trump could rescue relations from the pit into which they were plunged after it annexed Crimea from Ukraine. Almost six months into the Trump presidency, there may be increasing pessimism.
But the Kremlin is calling Mr Trump's meeting with Mr Putin on Friday an important chance to get acquainted. Perhaps it is betting that personal dynamics will help overcome policy differences.
After all, officials here insist that it is simply "Russophobia" in the US that has prevented President Trump "getting along" with Russia as he said he wanted.
They have certainly noted how in Poland he shied away from accusing Russia unequivocally of meddling in the US elections. Moscow has argued all along that there is no proof. In public at least, Mr Trump appeared to agree with that.
The US leader also hailed Poland as an example of a country ready to defend Western freedoms.
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Poland's conservative government shares Mr Trump's hostile view of immigration and strong sense of sovereignty.
Russian TV dismisses Poland visit - BBC Monitoring
NTV correspondent - "After the icy reception [Trump] was given in Europe in May what he needs now are comfortable and favourable surroundings, a picture along the lines of 'look at how they adore us here'."
Ren TV presenter - Trump was keen to play on differences within Europe and help Poland "cobble together an Eastern European bloc opposed to EU leaders... Trump is only too happy to pour oil onto the fire of European discord."
[BBC SOURCES]
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