The anti-corruption campaigner fell ill during a flight and the plane made an emergency landing in Omsk, Kira Yarmysh said, adding that they suspected something had been mixed into his tea.
The hospital said Mr Navalny was in a stable but serious condition.
Mr Navalny, 44, is a staunch critic of President Vladimir Putin.
In June he described a vote on constitutional reforms as a “coup” and a “violation of the constitution”. The reforms allow Mr Putin to serve another two terms in office.
What has the spokeswoman said?
Kira Yarmysh, the press secretary for the Anti-Corruption Foundation, which Mr Navalny founded in 2011, tweeted: “This morning Navalny was returning to Moscow from Tomsk.
“During the flight, he felt ill. The plane made an urgent landing in Omsk. Alexei has toxic poisoning.”
She added: “We suspect that Alexei was poisoned by something mixed into [his] tea. It was the only thing he drank since morning.
“Doctors are saying that the toxic agent absorbed faster through the hot liquid. Right now Alexei is unconscious.”
Ms Yarmysh later tweeted that Mr Navalny was on a ventilator and in a coma, and that the hospital was now full of police officers.
She said doctors were initially ready to share any information but were now saying the toxicology tests were delayed and were “clearly playing for time, and not saying what they know”.
She said in a tweet at 14:58 local time (08:58 GMT) that Mr Navalny’s condition had not changed and he was still unconscious.
What are the other reports from the scene?
The Tass news agency quoted one source at the Omsk Emergency Hospital as saying: “Alexei Anatolyevich Navalny, born in 1976. Poisoning intensive care.”
However, the deputy head physician of the hospital later told media that it was not certain Mr Navalny had been poisoned, although “natural poisoning” was one of the diagnoses being considered.
Anatoly Kalinichenko said Mr Navalny was in a stable and serious condition, but did not comment on the threat to his life.
Video footage on social media shows Mr Navalny being taken on a stretcher to an ambulance on the airport runway.
Other disturbing video appears to show a stricken Mr Navalny in pain on the flight.
Passenger Pavel Lebedev said: “At the start of the flight he went to the toilet and didn’t come back. He started feeling really sick. They struggled to bring him round and he was screaming in pain.”
Another photograph on social media purports to show Mr Navalny drinking from a cup at a Tomsk airport cafe.
The Interfax agency said the cafe owners were checking CCTV to see if it could provide any evidence