Former interior minister and leading opposition figure Yuriy Lutsenko was among those wounded.
Lutsenko was hurt while reportedly trying to mediate between the protesters and riot police.
Reports said at least 10 people were injured.
Supporters of the three men -- Ihor Mosiychuk, Volodymyr Shpara, and Serhiy Bevz -- had gathered outside the court earlier on January 10 to protest the ruling against them, claiming the trial had been a sham.
The violence broke out after the 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.
The BBC's David Stern, in Kiev, says that while the ongoing protests have produced the largest demonstrations since the 2004 Orange Revolution, so far none of the protesters' main demands have been met.
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 organization.
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, 49, who was reportedly hit on the head.
Mr Lutsenko was a prominent member of jailed former PM Yulia Tymoshenko's pro-Western government.
He himself was jailed for embezzlement and abuse of office in 2010, but pardoned under EU pressure in April 2013.
Mr Lutsenko's wife Irina said her husband had suffered concussion after being attacked by baton-wielding police as he tried to break up the violence and had been placed "in intensive care".
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, our correspondent says.
The latest scuffles underscore the continuing tension between the demonstrators and President Yanukovych, our correspondent adds.
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 Chornovil, 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 Chornovil.
Source: BBC News