Mr Kalashnikov had been involved in the "anti-Maidan" protests in support of deposed President Viktor Yanukovych.
It is not clear if he was murdered or committed suicide. Police say an investigation has been launched.
At least eight Yanukovych allies have died suddenly in the last three months.
Most of the deaths are said to have been suicides. However, officials say it was possible some were killed or forced to take their lives.
Commentators in Ukraine have accused supporters, as well as opponents, of the current pro-Western government of involvement in the deaths.
The BBC's David Stern in Kiev says no motive has emerged linking the deaths and no arrests have been made.
Mr Kalashnikov was a former deputy in parliament and a member of Mr Yanukovych's Party of Regions.
Accounts of his death differ, with some sources saying his body was found outside his flat in Kiev and others saying it was found within.
Mr Yanukovych fled Ukraine in February last year, after months of increasingly violent protests against him, centred on the Maidan, Kiev's main square.
He later reappeared in Russia. The government that succeeded him reversed his opposition to closer ties with the European Union - a major factor behind the protests.
It has since been plunged into a conflict with pro-Russian separatist rebels in the country's east.
A Ukrainian opposition politician, Oleg Kalashnikov, has been found dead with gunshot wounds in Kiev - the latest ally of the former government to have died in suspicious circumstances.