The Donetsk and Luhansk regions are territories in dispute between the Ukrainian government and pro-Russian separatists.
Negotiations to stop the fighting resulted in agreements for a ceasefire, though the fighting continues.
Another part of the accord known as the Minsk Protocol is for the decentralization of power in Donetsk and Luhansk. This is the point the Ukrainian parliament was acting upon.
But protesters against decentralization massed by the parliament building in Kiev, and violence broke out after the first round of voting on the measure.
A police representative said that supporters of a political party attacked the parliament building and police confronted them.
Protesters threw a grenade at police, lawmaker Anton Gerashchenko said via Facebook.
Interior Minister Arsen Avakov said at least 90 people were injured, four in critical condition, and one police officer died.
The person who threw the grenade was among 30 people who were arrested, Avakov said.
"He had other shells on him. There will be other arrests," the interior minister said.
Wednesday's vote moved forward a proposed constitutional amendment to decentralize power and allow self-government in the separatist-controlled regions.
The amendment is not a done deal. The Constitutional Court will have to review it, and parliament will have to pass it with 300 votes out of 450 this winter.