Milashina, who works for the Novaya Gazeta newspaper, told the Dozhd television channel late on February 3 that her chief editor, 2021 Nobel prize winner Dmitry Muratov, and some "high-level sources" have insisted that she leave the country because the level of danger she faces is "high enough."
Milashina, who writes about human rights abuse in Chechnya, added that she will continue her work from abroad.
Kadyrov has openly called Milashina and a member of the presidential council on human rights Igor Kalyapin "terrorists," stressing that Chechen authorities "have always liquidated terrorists and their accomplices."
Kadyrov's close associate, a member of the Russian State Duma, Adam Delimkhanov, also threatened Milashina and Kalyapin earlier this week.
Novaya Gazeta's leadership turned to the Investigative Committee, urging it to launch a probe against the Chechen leadership on a charge of inciting hatred and is awaiting a response.
Russian and international human rights groups have for years accused Kadyrov of overseeing grave human rights abuses including abductions, torture, extrajudicial killings, and the persecution of the LGBT community.
Kremlin critics say Russian President Vladimir Putin has turned a blind eye to the abuses and violations carried out by Kadyrov because he relies on the former rebel commander to control separatist sentiment and violence in Chechnya.
Chechnya went through two devastating post-Soviet wars and an Islamist insurgency that spread to other mostly Muslim regions in the North Caucasus.