The lawsuit contends that Ronaldo met Mayorga at a Las Vegas nightclub in June 2009 and the next night invited a group of people, including Mayorga, back to the penthouse suite where he was staying.
Kathryn Mayorga, a 34-year-old former model, has claimed the famous footballer assaulted her in Las Vegas in 2009.
His absence from the national team means he will miss the UEFA Nations League game against Poland on October 1 and a friendly against Scotland in Glasgow three days later.
Five-time Ballon d'Or victor Ronaldo, who joined Juventus for £99.2m in July, has scored 85 goals in 154 games for his country and won Euro 2016.
Meanwhile, Ronaldo's lawyer has previously said: "The reporting in Spiegel is blatantly illegal".
Ms Mayorga, the 34-year-old former USA teacher, was inspired to speak out by the #MeToo movement, her lawyer said.
The US sportswear giant - which has a contract worth a reported $1bn (£768m) with Ronaldo - said it would "continue to closely monitor the situation", the Associated Press reports.
"My clear conscience will thereby allow me to await with tranquility the results of any and all investigations", he said in a second Twitter post.
"She wants justice, of course", he said.
"While screaming "no, no, no" she was sodomized by Cristiano Ronaldo", the document reads.
Ronaldo, a father of four who initially made his name in the game during a six-year spell at Manchester United, transferred to Juventus from Real Madrid in the summer in a €100-million (US$115 million) deal.
However, the Portugal football player who also plays for Italian club Juventus, denied the allegation and ready to face any investigation in connection with the case.