Kiev's Espreso television said Radical Party member Igor Mosiychuk was walking out of its studio after giving an interview Wednesday when an explosive device went off near a scooter parked on the street.
The Ukrainian interior ministry said Mosiychuk's bodyguard died on the way to the hospital and a passerby was killed at the scene.
Security Service of Ukraine (SBU) spokeswoman Olena Gitlyanska told AFP a terror probe had been launched but that "the investigation is looking into all versions" of events.
"Clearly, this is the work of our enemy's secret services," he said in an apparent reference to Russia.
The blast was the latest in a series of bombings to have hit the Ukrainian capital targeting politicians and a journalist.
Former Russian lawmaker Denis Voronenkov -- a Kremlin critic who had moved to Kiev -- was gunned down in broad daylight in the Ukrainian capital in March.
A car bomb killed journalist Pavlo Sheremet in July 2016. The independent Ukrainska Pravda news site's reporter had denounced the political courses taken by both Russia and Ukraine.
The Radical Party stands in nominal opposition to the government but has also been willing to work with it in the past.
Mosiychuk himself spent 2011-2014 in jail after being convicted of involvement in an ultra-nationalist "terrorist" group.
The 45-year-old was released from prison after Ukraine's February 2014 pro-EU revolt.
He was further embroiled in a 2015 bribery case that was eventually dropped.
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