The Spaniard tested positive for the performance-boosting substance darbepoetin after winning the 50km classical cross-country in Salt Lake City.
He was caught along with Russians Larissa Lazutina and Olga Danilova, both of whom tested positive for the same drug and were also disqualified.
He was subsequently stripped of the medal, although he was allowed to keep two other golds he won at the Games because he won them before testing positive.
CAS confirmed on Monday that Muehlegg had launched an appeal.
"In accordance with the CAS procedural rules, the athletes and the International Olympic Committee will have the opportunity to submit their arguments in writing," the organisation said in a statement.
The tribunal could take up to four months to rule on whether Muehlegg gets his medal back.
Earlier on Monday, the Norwegian Olympic Committee and several Norwegian athletes lodged their own appeal with the CAS.
They called for athletes caught doping at Salt Lake to be stripped of all their medals and singled out Muehlegg, Lazutina and Danilova.