Khodorkovsky has vowed to continue protesting until Medvedev confirms he is aware of the situation.
Vadim Klyuvgant, Khodorkovsky's defence lawyer, said: "Since you cannot achieve anything with legal means, the man is forced to take such a step, and we hope that this message, albeit delivered in such an extreme way, will be finally heard, and that this will not affect the state of our defendant."
The hunger strike began on Monday, Maxim Dbar, a spokesman for Khodorkovsky's legal team, said.
"He is not worried about his own conditions. He is afraid the decision will become a precedent for others charged with economic crimes," Dbar said.
The Moscow court extended Khordorkovsky’s detention by three months in a new trial that could see him behind bars for 22 years on charges of theft and money laundering.
Medvedev signed a law banning the pre-trial detention of suspects accused of economic crimes after the death in prison of a tax lawyer awaiting trial drew international condemnation.
Khodorkovsky’s supporters have repeatedly staged protests outside the court hearings.
They have said that the case is politically motivated - part of a state crackdown on opponents of Putin, the former president turned prime minister.
Neave Barker, Al Jazeera's correspondent in Moscow, said: "Human rights groups are petitioning the president to rule directly on the situation. Khodorkovsky has appealed in an open letter to the supreme court ... and his lawyers have appealed to the Moscow court. They say they will deliver their verdict on Friday.
"But whether or not as Khodorkovsky hopes, Medvedev will know about it is anybody's guess."
Khodorkovsky was once head of Russia’s second biggest oil company.
The Russian government insists Khodorkovsky committed massive financial crimes to acquire his fortune.