He was taken from the remand prison without any notification being given to his supporters and may have been sent to a prison camp, they added.
Earlier this month a Moscow court converted a 2014 suspended sentence for embezzlement into a prison term.
The original conviction was widely seen as politically motivated.
Navalny is the most ferocious critic of the Russian authorities under President Vladimir Putin.
Last summer he was poisoned in Siberia with a chemical nerve agent. An independent investigation has alleged that a hit squad of Russian security agents tried to kill him.
In a coma he was airlifted to Germany, where he recovered. He returned to Russia in January and was arrested on arrival.
The court this month found that he had violated the terms of his probation over the embezzlement case, and imposed the sentence of nearly three years.
In another development, EU leaders condemned Navalny's treatment on Thursday and demanded his immediate release.