The 40-year-old former midfielder, who won the World Cup and two European championships with Spain, revealed news of his positive test ahead of Al-Sadd's home game with Al-Khor.
"Today I won't be able to join my team on their comeback to the official competition," Xavi wrote on Al-Sadd's Twitter account. Reserve team coach David Prats will deputise.
"A few days ago, I tested positive in the last Covid-19 test.
"Fortunately, I'm feeling okay, but I will be isolated until I am given the all-clear.
"When the health services allow it, I will be very eager to return to my daily routine and to work."
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Every season of Messi as he wins La Liga golden boot for seventh time
Lionel Messi is set to leave Barcelona after 20 years of winning silverware and setting records. Here are his stats, season by season.
2004/05 - Barcelona - La Liga: 7 apps; 1 goal. All competitions: 9 apps; 1 goal.
2005/06 - Barcelona - La Liga: 17 apps; 6 goals. All competitions: 26 apps; 8 goals. Trophies: La Liga, Champions League.
2006/07 - Barcelona - La Liga: 26 apps; 14 goals. All competitions: 36 apps; 17 goals. Trophies: Spanish Super Cup.
2007/08 - Barcelona - La Liga: 28 apps; 10 goals. All competitions: 40 apps; 16 goals. Trophies 0.
2008/09 - Barcelona - La Liga: 31 apps; 23 goals. All competitions: 51 apps; 38 goals. Trophies: La Liga, Copa del Rey, Uefa Champions League.
2009/10 - Barcelona - La Liga: 35 apps; 34 goals - top scorer. All competitions: 53 apps; 47 goals. Trophies: Spanish Super Cup, Uefa Super Cup, Fifa Club World Cup, Ballon d'Or, La Liga.
2010/11 - Barcelona - La Liga: 33 apps; 31 goals. All competitions: 55 apps; 53 goals. Trophies: Spanish Super Cup, Ballon d'Or, La Liga, Uefa Champions League.
2011/12 - Barcelona - La Liga: 37 apps; 50 goals - top scorer. All competitions: 60 apps; 73 goals. Trophies: Spanish Super Cup, Fifa Club World Cup, Ballon d'Or, Copa del Rey.
2012/13 - Barcelona - La Liga: 32 apps; 46 goals - top scorer. All competitions: 50 apps; 60 goals. Trophies: La Liga.
2013/14 - La Liga: 31 apps; 28 goals - top scorer. All competitions: 46 apps; 41 goals. Trophies: Spanish Super Cup.
2014/15 - Barcelona - La Liga: 38 apps; 43 goals. All competitions: 57 apps; 58 goals. Trophies: Copa del Rey, La Liga, Uefa Champions League.
2015/16 - Barcelona - La Liga: 33 apps; 26 goals. All competitions: 49 apps; 41 goals. Trophies: Uefa Super Cup, Fifa Club World Cup, Ballon d'Or, Copa del Rey, La Liga.
2016/17 - Barcelona - La Liga: 34 apps; 37 goals - top scorer. All competitions: 52 apps; 54 goals. Trophies: Spanish Super Cup, Copa del Rey.
2017/18 - Barcelona - La Liga: 36 apps; 34 goals - top scorer. All competitions: 54 apps; 45 goals. Trophies: Copa del Rey, La Liga.
2018/19 - Barcelona - La Liga: 34 apps; 36 goals - top scorer. All competitions: 50 apps; 51 goals. Trophies: Spanish Super Cup, La Liga
2019/20 - Barcelona - La Liga: 33 apps; 25 goals - top scorer. All competitions: 44 apps; 31 goals.
2020/21 - Barcelona - La Liga 35 appearances, 30 goals - top scorer. All competitions: 47 apps, 38 goals. Trophy: Copa del Rey