"He is in a serious condition," the hospital's chief doctor Alexander Murakhovsky told TASS.
Yarmysh said police had been called to the hospital at their request.
"We think that Alexei was poisoned with something mixed in his tea. That was the only thing he drank in the morning," she wrote on Twitter.
The head of the legal department of the Anti-Corruption Foundation that Navalny heads, Vyacheslav Gimadi, wrote on Twitter that "there is no doubt that Navalny was poisoned for his political position and activity."
He said Navalny's lawyers were requesting an investigation into the attempted assassination of a public figure.
Navalny has suffered physical attacks in the past.
And he is the latest in a long line of domestic Kremlin critics to suffer an apparent poisoning.
Alexei Navalny endured chemical burns to his eye in 2017 when attackers threw green dye used as a disinfectant at his face outside his office.
In August last year, Navalny suffered rashes and his face became swollen while he was in a police detention center serving a short term for calling for illegal protests.