Parubiy was shot dead in the western city of Lviv on Saturday local time and President Volodymyr Zelenskiy said on Monday a suspect had been arrested for what he called "a horrific murder" that impacted "security in a country at war".
"We know that this crime was not accidental. There is Russian involvement. Everyone will be held accountable before the law," police chief Ivan Vyhivskyi said on Facebook.
Russia has not commented on the killing or on the suggestion it was involved in the incident.
Ukrainian Interior Minister Ihor Klymenko said on the Telegram messaging app the suspected shooter had been detained overnight in the Khmelnytskyi region in western Ukraine.
"Many details cannot be shared at this time," Klymenko said. "I will only say that the crime was carefully planned: the victim's movements were studied, a route was mapped out, and an escape plan was thought through."
Police chief Vyhivskyi said the suspect had disguised himself as a courier and had opened fire on Parubiy in broad daylight, firing his weapon eight times.
The shooter even made sure that the victim was dead, Vyhivskyi added.
"He spent a long time preparing, watching, planning, and finally pulling the trigger. It took us only 36 hours to track him down and arrest him," Vyhivskyi added.
Police published two photographs from the scene of the arrest that show two special forces officers holding a handcuffed man by the arms. Naked to the waist, he has his back to the camera and his face is not visible.
Parubiy, 54, was a member of Ukraine's parliament and had served as parliamentary speaker from April 2016 to August 2019.
He was one of the leaders of protests in 2013-14 demanding closer ties with the European Union that led to the ousting of Ukraine's then pro-Russian president, Viktor Yanukovich.
Parubiy was also secretary of Ukraine's National Security and Defence Council from February to August 2014, a period when Russia annexed the Crimea peninsula and Moscow-backed separatists began fighting government forces in eastern Ukraine.
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