The former goalkeeper's wife spoke of her "shock" after the 46-year-old developed symptoms "really fast".
⚠️ Read our coronavirus live blog for the latest news & updates
Recber was the star of the show as Turkey reached the 2002 World Cup semi-finals.
The former Barcelona keeper remains as his country's most capped player after making 120 appearances.
But his wife, Isil, revealed on Instagram that the ex-Fenerbahce star has been struck down by coronavirus.
She said: "I would have liked to give you better news while being transparent about the truth but I'm sorry to say that my husband is hospitalised with the diagnosis of Covid-19.
"Everything was normal when he suddenly developed symptoms really fast and we are still in shock.
"These are critical and difficult times.
"My only request is for people to be respectful during this process.
"My test was negative along with my son and daughter.
"He's in hospital and we are not allowed to see him.
"This is the most difficult part, not being able to be with him.
"God is great and he's entrusted to Turkish doctors. These days will pass too.
"Please do not spare your prayers #YouAreStrongRR."
Barcelona showed their support on Twitter as they wrote: "Get well Rustu! We love you and we as Barcelona stand with you!"
Fenerbahce posted: "We convey our wishes for a speedy recovery to our former national team goalkeeper Rustu Recber who sported our jersey for many years.
"We wish for him to regain his health as soon as possible and we hope to receive good news from him."
CORONAVIRUS CRISIS - BE IN THE KNOW
Get the latest coronavirus news, facts and figures from around the world - plus essential advice for you and your family.
To receive our Covid-19 newsletter in your inbox every tea time, sign up here.