The head of virology at the hospital, José Manuel Echevarría, said the man had tested positive for malaria, El País newspaper reported.
Another person admitted to Carlos III hospital on Thursday — a patient who had contact with the Spanish nurse with Ebola Teresa Romero — has also tested negative for the disease after being admitted with fever.
Doctors are still waiting on test results for a third person, a missionary returned from Liberia.
Separately, on Tenerife in Spain's Canary Islands, a Red Cross worker who had travelled from another affected country, Sierra Leone, was hospitalized, the organization said.
Health officials said on Friday the man was suffering from malaria.
This makes it less likely he is suffering from Ebola but tests will still be carried out at Madrid's Carlos III hospital, they added.
The Air France passenger was admitted to hospital after Spain on Thursday activated emergency health procedures at Madrid's Adolfo Suárez Madrid-Barajas airport when the flight crew reported the passenger's complaints to ground staff.
An Air France spokesperson told The Local the passenger — who was coming from Nigeria and was on a connecting flight from Paris, according to Spanish broadcaster RTVE — had now been isolated for medical checks.