His comments came after Ukraine's human rights ombudsman raised alarm about the state of health of the former prime minister, saying she had been unable to get out of bed at the weekend yet was still being interrogated in her cell.
Yanukovych said at a news conference with his Lithuanian counterpart Dalia Grybauskaite that he had reviewed the issue since the morning and had held talks with the Ukrainian health minister, interior minister and prosecutors.
He said he was informed by them that "the healthcare system in prison has not yet reached a sufficient standard, the care must be given in medical establishments in Kiev outside prison."
"This is likely to be done today or tomorrow," he added.
Rights ombudsman Nina Karpacheva said she visited Tymoshenko in her Kiev prison cell on Sunday night and was shocked to discover that the 50-year-old former premier was too weak to get out of bed.
"Her condition is extremely serious. She could not get out of bed when talking to me," Karpacheva said in comments released by her office. "She needs to be examined and treated outside of prison."
Tymoshenko was first placed under arrest on August 5 before she was sentenced to seven years in jail on October 11 for abuse of authority for agreeing gas contracts with Russia in 2009.
She has insisted that her prosecution was ordered by her arch-foe Yanukovych, who defeated her and other leaders of the 2004 Orange Revolution in the 2010 presidential election.