Pyotr Verzilov, an activist with Russian protest group Pussy Riot, is reported to have been taken to hospital in a serious condition.
Relatives speaking to the Meduza website said they believed he may have suffered poisoning but there is no official word on his condition.
He reportedly fell ill after a court hearing on Tuesday for fellow Pussy Riot activist Veronika Nikulshina.
Mr Verzilov was one of the activists who invaded the World Cup final pitch.
He is a dual citizen of Russia and Canada. On Thursday, Canadian Prime Minister Justin Trudeau said the situation was a "concern, obviously, given actions of recent months by the Russians in the UK" - referring to the poisoning of a Russian ex-spy and others in Salisbury.
However, he added it was "too early to draw any conclusions about what has happened or how it has happened". Mr Trudeau said consular officials had contacted the facility where Mr Verzilov was being treated.
Ms Nikulshina told Meduza that Mr Verzilov had complained of losing his sight, "then the ability to talk, then the ability to walk".
She said that when he was admitted to hospital, an initial examination "didn't turn up anything bad", but that later doctors suddenly moved Mr Verzilov to the hospital's toxicology wing.
Relatives quoted by Meduza say he still cannot speak and "reacts only with his eyes".
A member of staff at Moscow's Sklifosovsky hospital later confirmed to AFP news agency that Mr Verzilov was in the intensive care unit in a "serious condition", but gave no further details.
Mr Verzilov is married to Nadezhda Tolokonnikova, the Pussy Riot member who was sentenced in 2012 to two years in jail for a performance at a Moscow cathedral.
Ms Tolokonnikova tweeted: "Pyotr may have been poisoned. In the toxicology department in a very serious condition."
Maria Alyokhina, another Pussy Riot member who was jailed along with Ms Tolokonnikova, also tweeted that Mr Verzilov was in intensive care.
Meduza said Mr Verzilov was in the toxicology department of a hospital in Moscow's Sokolniki district.
It said Mr Verzilov's mother had not been allowed to see her son.
Mr Verzilov was part of the Voina performance art group with Ms Tolokonnikova before it split in 2009 and then acted as spokesperson for Pussy Riot during the 2012 trial.
He was jailed for 15 days this year along with three women activists after they staged a pitch invasion at the football World Cup final in Moscow on 15 July, wearing police uniforms.
They said the action, done in the name of Pussy Riot, was a protest against human rights abuses in Russia.