Hazard has featured just 25 times in all competitions for Madrid since arriving from Chelsea for €100 million in June last year, scoring two goals and supplying four assists. In his final campaign at Stamford Bridge, he registered 16 goals and 15 assists in the Premier League alone.
Hampered by injuries and fitness issues in the Spanish capital, Belgium boss Martinez bemoaned Hazard's latest setback.
"Obviously we were all delighted to see Eden [Hazard] play in the last three games with his club and starting to look happy and free, being able to score," Martinez told reporters.
"I think we were all looking forward to seeing Eden play for the national team. I think that was good news for the club as well because to be able to play minutes and get games will help his match fitness.
"The positive [Covid-19 test] is a disappointing news but it's not abnormal in the current world we live in. I think being positive for coronavirus is not news anymore.
"At the moment, we are just following the protocols of UEFA and making sure that Eden carries on working at home so he doesn't lose any fitness and see how quickly he can join the national team, if it can happen.
"But no, nothing mysterious about his positive [result], nothing at all. He's asymptomatic and he feels in good spirits and that's the only thing that matters."
The Blancos winger has gone more than a year without playing for Belgium by the time of his next cap because of injury and now virus concerns.
"One year is indeed a long time," Dortmund star Thorgan Hazard said of his older brother's absence. "I hope this will be over soon. Both Belgium and Madrid miss Eden.
"He is one of the best players in the world and it is always better to have him in your squad. Madrid lost last weekend without him and the Red Devils were also defeated in England. We all need an Eden at 100 per cent."