On Wednesday Judge Olga Nedelina ruled that Aleksanian's trial for fraud and money laundering would be halted while he was treated for cancer, but Nedelina turned down appeals that he be treated outside of jail.
The move comes after human rights experts and politicians both in the country and abroad accused the authorities of failing to give Aleksanian proper treatment.
In Brussels on Wednesday, a group of European parliament deputies issued an open letter to Vladimir Putin, the Russian president, urging him to allow hospital treatment for Aleksanian.
"The arrest of Vasily Aleksanian and the refusal to guarantee him adequate medical treatment may cause his death," said the letter from 23 ministers of the European Parliament (MEPs).
The MEPs also said the ruling was a "grave violation of the fundamental right to life".
Aleksanian's lawyers said their client is almost blind and suffering from lymphatic cancer and Aids.
Drew Holiner, one of his lawyers, said in a statement that his client needed "a combination of complex care including anti-retroviral therapy, medicine against tuberculosis and intensive chemotherapy in a specialised centre".
Aleksanian had been denied the treatment for 14 months, Holiner added.
The former vice-president at Yukos was arrested in April 2006.