Computers and documents were destroyed in the attack, according to a statement on Memorial’s website.
Memorial said a CCTV camera recorded the two men entering its office building at night in Nazran, a town in the Republic of Ingushetia in the North Caucasus, and throwing canisters into the group’s work place through an internal window.
Footage seen by AFP shows a man in a balaclava using a ladder to adjust a security camera on the building.
The group published photos of the aftermath of the fire, including a photo of a bottle it believes contained a flammable substance.
Last week, Chechnya detained the director of the local Memorial branch Oyub Titiyev for drug possession that activists say are bogus. The case has received international condemnation.
Memorial speaks about human rights violations in Russia and has specifically accused Chechen strongman Ramzan Kadyrov of heading a totalitarian regime that uses kidnapping and torture.
The rights group said the link between the arson attack in Ingushetia and “those forces who are trying to destroy the work of Memorial in Chechnya and pressure the organisation as a whole in the North Caucasus is obvious.”
It added that it considers the arson attack a “terrorist act” and called on local authorities to investigate.
But the Kremlin dismissed the link between the two cases.
“I don’t think that such conclusions can be drawn on the bases of a famous Memorial director in Chechnya stopped with drugs,” the Kremlin’s spokesman Dmitry Peskov said Wednesday.
“These are two different republics, two different subjects of the Russian Federation,” Mr. Peskov added.
Mr. Kadyrov is an ally of Russian President Vladimir Putin and has ruled Chechnya with an iron fist for a decade.
The Council of Europe’s Human Rights Commissioner Nils Muiznieks on Wednesday condemned the “succession of events that illustrates the threatening climate” for human rights defenders in the North Caucasus.
Attacks on rights groups in Russia’s volatile North Caucasus are not uncommon.
In 2014 the office of human rights organization the Joint Mobile Group was torched after it criticised the Kremlin-installed Chechen leader for calling for collective punishment against families of Islamist insurgents.