It marked the first anniversary of president Viktor Yanukovych, being ousted.
The Interior Ministry said the blast in the eastern city of Kharkiv was due to an “unknown explosive device” and was being considered a terrorist act. One of the two people killed was a police officer.
The violence comes as bloodshed continues stemming from Mr Yanukovych’s fall a year ago. The Ukrainian parliament voted on 22 February last year to remove the Russia-friendly president, following months of increasingly violent protests in the capital Kiev.
The Crimean peninsula, where residents largely regarded his downfall as a coup, was annexed by Russia a month later.
Then armed rebels opposed to the new authorities in Kiev took over large parts of two regions bordering Russia, setting off a war that has killed more than 5,600 people.
A peace plan detailing a ceasefire and pullback of heavy weapons was signed ten days ago, but has been continually violated.
Ukraine was planning to begin pulling back heavy weaponry from the frontline yesterday in accordance with the peace plan, a military spokesman said.
A spokesman for the separatists said the pullback from both sides was to take place between yesterday and 7 March but he did not specify whether rebels had made any moves yet.
Both sides are to pull back their big guns and rockets from 15 to 43 miles away from the conflict line – depending on the weapons’ size – creating a buffer zone of between 31-87 miles.
The buffer zone was a main element of a peace agreement worked out in marathon negotiations ten days ago in the Belarusian capital Minsk.
It also calls for a full exchange of war captives. Late on Saturday, 139 Ukrainian soldiers and 52 rebels were exchanged. It remains unclear how many prisoners in total are on each side and when other swaps might take place.
The ceasefire came into effect last Sunday. Ukraine said yesterday Russian-backed separatists violated it a dozen times during the night with artillery and rocket attacks and an attempt to storm a Ukrainian encampment.
A spokesman said one serviceman had been killed and three had been wounded over the past day.
Explosions were heard in the main rebel-held city Donetsk around dawn yesterday morning and a rebel website said several buildings in the city were damaged by artillery.
Despite the reported violations, the level of firing appeared to be far lower than a week ago.
Among the attacks reported by the Ukrainian military was an attempt to storm positions in the village of Shyrokyne near the port city of Mariupol.
The city remains of strategic concern to Ukraine because if it was seized by rebels, it could help establish a land corridor between mainland Russia and the annexed Crimean peninsula.
Kharkiv, where yesterday’s explosion took place, has symbolic importance relating to Mr Yanukovych’s ouster.
Part of the heavily industrialised east that had been his base of support, the city was the last place he was publicly seen in Ukraine before surfacing in exile in Russia.
He had fled Kiev the evening before, and in Kharkiv he gave a video interview bitterly likening the protesters against him to Nazis.
Opponents of the new Kiev regime seized some buildings in Kharkiv before they were returned to government control.