The murder of the 55-year-old politician, who has been an outspoken critic of Russia's involvement in Ukraine, came ahead of a major opposition rally this weekend.
US President Barack Obama condemned the "vicious murder" of Nemtsov, whom he had met on a visit to Moscow, and called on the Russian government to conduct a prompt and impartial investigation of the killing.
The Kremlin swiftly dubbed his death a provocation.
The murder "bears the hallmarks of a contract killing," Putin spokesman Dmitry Peskov said, adding it was a provocation.
"According to preliminary information, an unidentified person shot at Boris Nemtsov no fewer than 7-8 times from a car as he was walking along the Bolshoi Moskvoretsky bridge," investigators said in a statement.
The Investigative Committee, which reports directly to Putin, confirmed Nemtsov's death, saying it had opened a criminal probe.
The committee said "experienced" investigators had been put on the case.
Nemtsov launched his political career as the governor of Nizhny Novgorod region in central Russia and became a vice prime minister in the late 1990s under the presidency of Boris Yeltsin.
After leaving parliament in 2003, he led several opposition parties and groups.
Nemtsov's murder comes ahead of a major opposition rally scheduled to take place on Sunday.
Interior Minister Vladimir Kolokoltsev has taken charge of the criminal probe.