The rally was one of several being held to mark a year since the Kiev uprising that led to the fall of pro-Russia leader Viktor Yanukovych.
Security forces have detained four suspects in the attack, officials say.
Kharkiv lies outside the conflict zone in eastern Ukraine, where a ceasefire appears finally to be taking hold.
The Ukrainian government has agreed to start pulling back heavy weapons from February 22, and the rebels said they would start the process on February 24.
The pullback will not be completed until at least March 8, five days later than the deadline set at peace talks in Minsk this month.
Another key element of the Minsk deal moved forward on February 21 when the Ukrainian government and the rebels exchanged 191 prisoners.
The ceasefire continues to be breached, notably in Debaltseve, a key transport hub captured by the rebels in recent days, an OSCE official said.
Alexander Hug added that the humanitarian situation there was “relatively catastrophic”.
“The local population reported to us that there is no water, no food, no gas, no heating, no electricity, no medication. And all the buildings that our monitors have seen (…) have been affected by the fighting,” he said.
The explosion in Kharkiv happened at 13:20 as people gathered near the city’s Palace of Sport for a march in support of national unity, Ukrainian media say.
Officials initially said an explosive device had been thrown from a car but later said it had been buried in the snow.
“Security service detained persons who may have been involved in the preparation and carrying out of crimes of a terrorist nature in Kharkiv, including the explosion,” security spokesman Markian Lubkivskyi wrote on his Facebook page.
He later said the four suspects were Ukrainian citizens who had received instruction and weapons in the Russian city of Belgorod, just across the border.
Markian Lubkivskyi also posted a picture of a rocket launcher which he said the suspects were planning to use in attacks in the city.
Ukrainian President Petro Poroshenko described the attack as “a bold attempt to expand the territory of terrorism” and promised to bring the perpetrators to justice.
Before Sunday’s explosion, Kharkiv, in the north-east of Ukraine, had seen more than a dozen attacks over three months, including an explosion in a bar used by pro-government activists which injured more than 10 people in November.
That attack was blamed on a pro-Russian group calling itself the Kharkiv Partisans.
Meanwhile, thousands of Ukrainians have been taking part in “dignity marches” in the capital Kiev and other cities, remembering the victims of sniper fire during protests last February.
European leaders including European Council president Donald Tusk, German President Joachim Gauck and the leaders of Lithuania, Poland and Moldova have been attending in Kiev.
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