Khodorkovsky has been refusing food and water for several days in the Moscow jail cell he shares with 10 other inmates.
In a statement read in part by Khodorkovsky's lawyer Anton Drel on NTV television, the billionaire claimed President Vladimir Putin's Kremlin was behind decisions by prison authorities to transfer Platon Lebedev to isolation and move him to a more crowded cell.
"On 19 August, my comrade Platon Lebedev was moved to a 32-square-foot isolation cell. Platon is seriously ill," the statement said. "It is obvious that they threw my friend into the isolation cell to avenge me, Mikhail Khodorkovsky, for my articles and interviews. Let the Kremlin think it is showing strength, in fact it is a display of their weakness and fear."
Mr Khodorkovsky, the 42-year-old founder of the Yukos oil company, was sentenced in May to nine years in jail for fraud and tax evasion. Mr Lebedev was given the same jail term.
Mr Khodorkovsky has criticised the Kremlin in a range of articles and interviews, and is said to be considering running in an upcoming parliamentary by-election.
Mr Lebedev's lawyers say he is not getting adequate medical treatment.
Mr Khodorkovsky said this week he would consider running for a vacant seat in the lower house of parliament in December.
The head of the central electoral commission, Alexander Veshnyakov, said Mr Khodorkovsky could register as a candidate before his sentence came into force. But the immunity granted for candidates would not free him from serving his current sentence.Reuse content