An unidentified attacker shot Mr Nemtsov four times in central Moscow, a source in the law enforcement bodies told Russia’s Interfax news agency.
He was reportedly shot near the Kremlin while walking with a woman.
He died just before a march in Moscow against the war in Ukraine which he was actively promoting.
In a recent interview, he had said he feared Russian President Vladimir Putin would have him killed because of his opposition to the war in Ukraine.
Mr Putin has condemned the killing, a Kremlin spokesman told news agencies.
Mr Nemtsov, 55, served as first deputy prime minister under the late President Boris Yeltsin in the 1990s.
He had earned a reputation as an economic reformer while governor of one of Russia’s biggest cities, Nizhny Novgorod.
Falling out of favour with Yeltsin’s successor, Mr Putin, Mr Nemtsov became an outspoken opposition politician.