"We are looking at the possibility that the murder was a contract killing," Anatoly Bagmet, Moscow's investigative committee head, said in televised remarks.
He said the killing could have been related to Kalmanovich's business affairs or driven by "personal revenge".
Jailed for spying
Born in then Soviet-controlled Lithuania in 1949, Kalmanovic immigrated with his family to Israel in the early 1970s, where he became a government adviser on the resettlement of Soviet Jews in Israel.
He reportedly agreed to spy for the KGB in return for permission to leave Lithuania.
In 1988 Israel convicted Kalmanovich of espionage and he was imprisoned.
He eventually returned to Russia where he made his fortune in construction, becoming director general of the large Tishinsky shopping centre in Moscow.
Kalmanovich used his fortune to sponsor three basketball clubs, becoming general manager of the Russian women's basketball team in 2008.
He was also known as a concert promoter who brought Michael Jackson, Liza Minnelli and Jose Carreras to Russia.