"According to initial information she was killed by two shots when leaving the lift. Neighbours found her body," said a police source. "Police found a pistol and four rounds in the lift.
Politkovskaya, a 48-year-old mother of two, won international fame and numerous prizes for her dogged pursuit of rights abuses by Putin's government, particularly in the violent southern province of Chechnya.
"The first thing that comes to mind is that Anna was killed for her professional activities. We don't see any other motive for this terrible crime," said Vitaly Yaroshevsky, a deputy editor of the newspaper where Politkovskaya worked.
Former Soviet President Mikhail Gorbachev, a shareholder in Politkovskaya's newspaper Novaya Gazeta, called the killing a "savage crime".
Amnesty International issued a statement saying it believed "that Anna Politkovskaya was targeted because of her work as a journalist, reporting on human rights abuses in Chechnya and other regions of the Russian Federation."
The human rights group called on Russian authorities "to investigate her murder thoroughly and impartially, to make the findings of the investigation public and for suspected perpetrators to be brought to justice in accordance with international law."
Moscow chief prosecutor Yuri Syomin told reporters at the crime scene, a nine-storey Soviet-era apartment building in central Moscow, that he was treating the death as murder.