An unidentified attacker in a car shot Mr Nemtsov four times in the back as he crossed a bridge in view of the Kremlin, police say.
He died hours after appealing for support for a march on Sunday in Moscow against the war in Ukraine.
Russian President Vladimir Putin has condemned the murder, the Kremlin says.
President Putin has assumed "personal control" of the investigation into the killing, said his spokesman Dmitry Peskov.
It "bears the hallmarks of a contract killing," said Mr Peskov.
US President Barack Obama condemned the "brutal murder" and called on the Russian government to conduct a "prompt, impartial and transparent investigation".
Ukrainian President Petro Poroshenko described Mr Nemtsov as a "bridge between Ukraine and Russia".
"The murderers' shot has destroyed it. I think it is not by accident," he said in a statement published on his administration's Facebook page.
Boris Nemtsov was one of Russia's leading economic reformers in the 1990s (file photo from 2009)
In a recent interview, Mr Nemtsov had said he feared Mr Putin would have him killed because of his opposition to the war in Ukraine.
Mr Nemtsov, 55, served as first deputy prime minister under 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, he became an outspoken opposition politician.