Both Xhaka and the doctor who approved the false certificate can now be punished, police in Lucerne said, according to DPA.
Switzerland will now have to do without their team captain during the upcoming Nations League.
"We have jointly concluded that it is in the best interests of the team to carry out this national team camp without him," said federation chairman Peter Knäbel in a statement.
It was in 2021 that Xhaka tested positive for Covid-19 and missed two matches with the national team. He later said that he had been vaccinated.
The 33-year-old is best known for his time at Arsenal, where he played from 2016 to 2023.
