In an interview with Die Welt am Sonntag newspaper, Frauke Petry also accused Ozil, a practising Muslim, of promoting a political agenda by posting a picture of himself on social media on a pilgrimage to the holy city of Mecca last month.
Her comments came a week after the AfD's vice-chairman provoked outrage by saying people would not want black German soccer star Jerome Boateng as their neighbour.
"It's a shame that Mesut Ozil, someone who so many children and young people identify with, does not sing the national anthem," Petry was quoted as saying in the paper.
Ozil, a third-generation Turkish-German, has been held up as a prime example of successful integration into German society, and has been a stalwart of the national side since 2009.
There was no immediate response from the Arsenal star. The online version of Der Spiegel magazine said German players have no particular tradition of singing along to the national anthem before kick-off, and it is not unusual for them to remain silent, irrespective of their religion.
Asked about Ozil's pilgrimage to Mecca, Petry accused him of hypocrisy and wanting to promote a political agenda.
"You might want to ask Ozil if he wanted to make a political statement," she said.
"He doesn't live according to the rules of Sharia. At any rate, the women who he appears with in public, don't wear a veil," she added, in an apparent jab at his lifestyle.
The AfD maintains that Islam violates the constitution and wants a ban on minarets and face veils.
The party has seen its support surge amid disenchantment with Chancellor Angela Merkel's open-door policy towards refugees fleeing conflicts and poverty in the Middle East and beyond. More than one million migrants arrived in Germany last year.
But the attacks on Germany's national team appear to have backfired on the party, with support for the AfD down 2 points to 12 percent, according to a poll published in Bild am Sonntag.
Germany's national team includes several other players of mixed ethnic background including defender Boateng, born in Berlin to a German mother and Ghanaian father, and Leroy Sane, whose father is former Senegalese international Souleyman Sane.