The Wikileaks founder’s lawyers had applied for him to be freed on bail because he was “vulnerable” to the virus inside HMP Belmarsh.
He is being held there while awaiting potential extradition to the US on charges relating to the 2010 Wikileaks publications over the Iraq and Afghanistan wars.
The court heard that despite coronavirus being confirmed in other jails, there were not yet an known cases in HMP Belmarsh.
Supporters of Mr Assange said he had a previously reported lung complaint and was in an “already weakened medical condition”.
American and British authorities class Mr Assange as a flight risk because he skipped bail over Swedish sexual assault allegations to flee to London’s Ecuadorian embassy in 2012.