Seen as President Vladimir Putin's most vociferous critic, Navalny was serving a 19-year jail term on charges widely considered politically motivated.
He was moved to an Arctic penal colony, said to be one of Russia's toughest jails, late last year.
The prison service in the Yamalo-Nenets district said Navalny had "felt unwell" after a walk on Friday.
He had "almost immediately lost consciousness", it said in a statement, adding that an emergency medical team had immediately been called and tried to resuscitate him but without success.
"The emergency doctors declared the prisoner dead. Cause of death is being established."
Navalny's lawyer Leonid Solovyov told Russian media he would not be commenting yet, although his close aide Leonid Volkov wrote on X: "Russian authorities publish a confession that they killed Alexei Navalny in prison. We do not have any way to confirm it or to prove this isn't true."
Navalny had long sought to challenge Vladimir Putin at the ballot box, but he was barred from running in the 2018 presidential election. Next month, Russia's leader will stand unchallenged by any meaningful opposition.
Anti-war candidate Boris Nadezhdin was banned from standing in the election because of supposed irregularities found in the thousands of signatures submitted in support of his candidacy.
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