Two women, a journalist and a director of an anti-Kremlin NGO, reported symptoms that suggested possible poisoning.
Navalny's supporters said last month that he was suffering from significant stomach pain in jail, which they said could be a sign of some sort of slow acting poison.
Navalny said it was absurd to argue he had committed terrorism while in prison.
Russian prison supervisors said that just two weeks ago, Navalny's health was not in danger.
Navalny was arrested two years ago immediately after returning to Russia from Germany where he received life-saving medical treatment.
Perhaps the most notable Putin critic in the world, Navalny is serving an 11.5-year prison sentence for his dissidence.