"Alexei Navalny's health condition is considered to be satisfactory. A general practitioner examines him every day," dpa news agency quoted the federal penitentiary authority as saying in a statement.
"The patient has given his consent that vitamins be prescribed to him," the statement said, adding that the hospital where he was moved is specialized in "dynamic observation of such patients".
Navalny has been on hunger strike for more than two weeks to protest the lack of medical care in the prison camp.
His team has repeatedly sounded alarms about his deteriorating health, warning of possible heart failure.
On Sunday, the US, the European Union, Germany and others urged the Russian leadership to provide adequate medical treatment to Navalny.
Washington also threatened consequences should the 44-year-old die in hail.
After surviving a Novichok nerve agent attack last year and receiving treatment in Germany, Navalny returned to Russia in January and was immediately arrested.
He blames the Russian state for the attack.
He has since been sentenced to a prison term on charges of violating parole for a 2014 fraud conviction while he was being treated in Germany.