|Mr Nemtsov was shot on bridge within sight of St Basil's Cathedral and Kremlin|
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.
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.
|Boris Nemtsov was one of Russia's leading economic reformers 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.
Thorbjorn Jagland, secretary general of the Council of Europe, condemned the killing, saying in a tweet: "I am shocked and appalled key opposition leader Boris Nemtsov was shot. Killers must be brought to justice."
US President Barack Obama condemned the "brutal murder" and called on the Russian government to conduct a "prompt, impartial and transparent investigation".
Mr Nemtsov was shot at around 23:40 (20:40 GMT) on Friday while crossing Bolshoy Kamenny Bridge accompanied by a woman, Russia's interior ministry said.
He was shot with a pistol from a white car which fled the scene, a police source told Russia's Interfax news agency.
According to Russian-language news website Meduza, "several people" got out of a car and shot him.
One of the politician's colleagues in his RPR-Parnassus party, Ilya Yashin, confirmed Mr Nemtsov's death.
"Unfortunately I can see the corpse of Boris Nemtsov in front of me now," he was quoted as saying by Russia's lenta.ru news website.
Flowers were left at the site of the shooting through the night.
|Russian opposition leaders Ilya Yashin, left, and Ksenia Sobchak |
react to news of the death of Mr Nemtsov.
I expect both are wondering if they will be next.
"If you support stopping Russia's war with Ukraine, if you support stopping Putin's aggression, come to the Spring March in Maryino on 1 March," he wrote.
Speaking earlier this month to Russia's Sobesednik news website, he had spoken of his fears for his own life.
"I'm afraid Putin will kill me," he said in the article (in Russian) on 10 February.
"I believe that he was the one who unleashed the war in the Ukraine," he added. "I couldn't dislike him more."
|Boris Nemtsov addresses the crowd at a rally in Moscow to oppose |
President Putin's policies in Ukraine - 15 March 2014
Almost 5,800 people have died and at least 1.25 million have fled their homes, according to the UN.
The Ukrainian government, Western leaders and Nato say there is clear evidence that Russia is helping the rebels with heavy weapons and soldiers.
Independent experts echo that accusation while Moscow denies it, insisting that any Russians serving with the rebels are "volunteers".
|Crimea was just the beginning for the ambitious Putin|
On the other hand, as with the Argentinian murder, it was so Mafia-like, one would be hard-pressed to believe that it was a professional hit by highly trained secret service. Perhaps both were attempts to discredit the respective Presidents. Perhaps, but I would be very surprised.