Former interior minister and leading opposition figure Yuriy Lutsenko was among those wounded.
The violence broke out after three activists were earlier jailed over an alleged terror plot.
The unrest took place amid ongoing anti-government rallies against the government's decision to pull out of a landmark deal with the European Union.
Instead, President Viktor Yanukovych struck a deal with Russia in December, which has seen big cuts in the price of gas imports from Russia.
Moscow also supported Ukraine's finances with a $15bn purchase of government bonds.
Lenin statue 'targeted'
The overnight clashes occurred outside a courthouse in Kiev, where a large crowd had gathered for the verdict in a trial against members of a far-right organisation.
Following the judgment, angry demonstrators blocked buses carrying police officers.
The situation escalated after protesters threw paint on the windscreens and started rocking the vehicles,
Local news reports showed footage of badly beaten protestors, including Mr Lutsenko who was reportedly hit on the head.
A large crowd had gathered near the courthouse in Kiev where the trial took place
Riot police reportedly detained several protesters during the violence
The altercations took place against the backdrop of ongoing anti-government protests
The three ultra-nationalists were handed six-year prison sentences on Friday for allegedly plotting to blow up a statue of the revolutionary Soviet leader Vladimir Lenin in 2011.
The far-right has played an active role in the pro-EU movement, which they see as a counterbalance to Russian influence in Ukraine, the BBC's David Stern, in Kiev, reports.
The latest scuffles underscore the continuing tension between the demonstrators and President Yanukovych, our correspondent says.
The country is experiencing its largest protests since the 2004 Orange Revolution.
Protesters have been camped out in Kiev's Independence Square since the opposition campaign began two months ago.
There have been occasional outbreaks of violence as police tried unsuccessfully to clear the square using tear gas.
The last major opposition protest at the end of December was given further impetus by an attack on activist and journalist Tetyana Chornovol, who was severely beaten up on Christmas Day.
She had accused Mr Yanukovych of corruption over his financing of his official residence outside Kiev.
Mr Yanukovych denied any allegation of corruption and called for an investigation into the attack on Ms Chornovol.
By BBC
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