Ukrainian police said the 52-year-old former deputy of Yanukovych's Party of Regions (PR) had been shot, although it was not yet clear whether it was murder or suicide. Police have opened an investigation.
Kalashnikov was a main supporter of the"anti-Maidan"demonstrations that backed the pro-Kremlin President Yanukovych before he was deposed in February last year. The anti-Maidan movement was formed in rebuttal to the Euromaidan protests that called for closer ties between Ukraine and the European Union, and ultimately led to Yanukovych's ousting.
Social media was rapidly awash with theories about the shooting. A Facebook post by senior ministry official Anton Gerashchenko mooted the idea that Kalashnikov had been murdered in connection with his knowledge of the backers and finances behind anti-Maidan.
Meanwhile, Ukrainian media suggested he had been killed by supporters of the new government – or its opponents.
Kalashnikov's death is the latest in a series of eight sudden deaths of Yanukovych allies and Party of Regions members in recent months. Most have been officially classed as suicides, including the deaths of senior Party of Regions member Mykhailo Chechetov, regional governor Oleksandr Peklushenko and former lawmaker Stanislav Melnyk.
The Guardian reported that Yanukovych's youngest son, also named Viktor, drowned in March 2015 when the van he was driving broke through ice on a lake in Siberia.
Yanukovych is reported to have fled to Russia. In January 2015, he was place on Interpol's most wanted list.