Officials said Assange seems thinner and "we are very concerned about his health," Voice of Russia Radio reported Thursday.
British authorities have said Assange would be arrested if he sets foot outside the embassy and has the diplomatic compound under around-the-clock police surveillance.
"If he falls ill, we will have to choose between two alternatives: to treat Assange in the embassy or hospitalize him," the vice minister said. "This is a very serious situation and it can affect Assange's human rights."
Ecuador has asked the British Foreign Office for a document that would enable Assange to enter hospital safely if necessary and return to the embassy with refugee status, the Voice of Russia quoted Albuja Martinez as saying.
Assange, who faces extradition from Britain to Sweden for questioning in a sexual assault case, has been in the Ecuador Embassy since August.
When the South American country granted Assange asylum, it said it shared his concerns that he could face charges in the United States over the publication by WikiLeaks in 2010 of thousands of secret U.S. diplomatic and defense communications.
The British Foreign Office said it was unaware of Assange's health problems, The Daily Telegraph reported.
"Ecuador has not told us that Mr. Assange is ill," a Foreign Office spokesman said. "However, were they to do so, we would consider the matter."