Igor Kalyapin, the head of the Committee to Prevent Torture rights group was ordered to leave his hotel on Wednesday evening and then targeted by a group of "young men in civilian clothes and black masks", a lawyer for the group said.
"They threw eggs, cake, flour and green disinfectant," Dmitry Utukin said.
Utukin posted a photograph on Facebook of Kalyapin standing with his face and jacket coated with flour and eggs and bright green disinfectant.
Kalyapin, a veteran activist, has publicised abuses by the Chechen strongman Ramzan Kadyrov. His group, which oversees rights activists in Chechnya, is one of the few still active in the region.
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The rights council said it wrote to Russia's interior minister Vladimir Kolokoltsev asking him to take personal control of the probe into the incident, which it said should be treated as the criminal offence of hooliganism.
Putin's spokesman Dmitry Peskov told journalists that "an attack on a member of the presidential council... Is a very dangerous trend, which undoubtedly prompts concern. This is unacceptable."
Peskov linked the attack to the crime-prone situation in the region, dismissing a suggestion that it could affect whether the Kremlin extends Kadyrov's mandate next month.
Earlier this month, masked attackers beat up foreign journalists and support staff and set fire to their minibus as they were driving to Grozny on a press tour organised by Kalyapin's group.
Kalyapin said a group of men entered his hotel room and ordered him to leave, citing his criticism of Kadyrov.
Outside a group of women shouted at him, asking how he dared to "speak badly of Ramzan," he said.
Kalyapin was visiting Grozny to meet journalists and a Chechen rights activist, his group said.
Last year the group's office in Grozny was attacked by masked men after it criticised Kadyrov's call to destroy the houses of relatives of suspected Islamists.