"Thank you so much for all the caring messages that I've received during these days," he wrote on his verified Instagram page alongside an image of him holding his daughter.
"I want to share with you that I'm recovered and back home with my family and the Al-Sadd team."
Xavi, 40, announced on Saturday that he had tested positive following routine screening of players and staff in Qatar's top-flight.
Exactly 4 percent of Qatar's 2.75 million people have had coronavirus, with 110,153 cases reported since the start of the pandemic giving the tiny Gulf state one of the highest per capita total infection rates.
However the gas-rich country has reported just 169 deaths meaning it has one of the world's lowest virus death rates and 106,849 people have recovered from COVID-19, according to official statistics.
Xavi missed Al-Sadd's 2-1 victory over Al-Khor, their first fixture since the resumption of the league which was suspended in March to contain the spread of COVID-19.
