A spokeswoman for Dmitry Medvedev, the Russian president, said he was outraged at Estemirova's death.
"The news was reported to the president, he was outraged and gave all appropriate orders to the head of the investigations commission [Alexander] Bastrykin," Natalya Timakova said.
"Natalya was providing invaluable information from the region, she was that one person whom the victims trusted fully"
Human Rights Watch
Earlier, Memorial said in a statement that Estemirova "was forcefully taken from her house into a car and shouted that she was being kidnapped" at 8.30am (0430 GMT) in Grozny, the Chechen capital.
The organisation said that Estemirova had planned a number of meetings on Wednesday, including a joint trip with the Chechen interior ministry.
"But she did not appear at the appointed places and she did not telephone," the statement said.
In 2007, Estemirova was awarded the Anna Politkovskaya prize - named after the murdered Russian journalist - by the Nobel Women's Initiative, a group established by female Nobel Peace Prize laureates.
She had also received awards from the Swedish and European parliaments.
Memorial and Human Rights Watch (HRW) had earlier this month issued a hard-hitting report accusing Chechen security forces of punishing families of alleged fighters by burning down their homes.
"Chechen authorities had expressed dissatisfaction with her work more than once," Memorial said.
HRW's Tatyana Lokshina, who worked with Estemirova in Chechnya, told Al Jazeera that she believes victims of abuse are now voiceless without her.
"This is a devastating personal loss ... she was instrumental to all of us - researchers, journalists, human rights defenders - everyone who would come to Chechnya on the job would talk to Natalya," she said.
"Natalya was providing invaluable information from the region, she was that one person whom the victims trusted fully ... without Natalya, they have no one to give them a voice. And this is something the Chechen government knew quite well."
Russia earlier this year ended a 10-year "counter-terrorism" operation in Chechnya, a mainly Muslim region riven by two separatist wars since the 1991 collapse of the Soviet Union.
Chechnya and other parts of the Russian Caucasus remain the site of a deadly insurgency led by Muslim fighters against the pro-Kremlin local authorities, who in turn have been accused of human rights abuses.
Security forces are being killed in clashes with fighters on an almost daily basis and last week 10 Chechen police officers were killed in an ambush in Ingushetia.