District Judge Vanessa Baraitser ordered the proceedings adjourned until Monday while a lawyer representing the U.S. government is tested for the virus.
Assange is fighting American prosecutors’ attempt to get the British government to send him to the U.S. to stand trial on spying charges.
U.S. prosecutors have indicted the 49-year-old Australian on 18 espionage and computer misuse charges over WikiLeaks’ publication of secret U.S. military documents a decade ago. The charges carry a maximum sentence of 175 years in prison.
Assange’s lawyers say the prosecution is a politically motivated abuse of power that will stifle press freedom and put journalists around the world at risk.
The hearing started Monday at London’s Old Bailey criminal court and is scheduled to last about a month.