The CAS said in a statement that a hearing would take place at its temporary offices in London on Friday with a final decision rendered early on Saturday.
The two athletes, national Olympic Committees, federations, International Olympic Committee and Games organisers LOCOG were invited to attend the hearing.
The Swedish Olympic Committee and Swedish Triathlon Federation want both athletes to be ranked as joint winners instead of just Spirig, who was declared the winner on a photo-finish on Saturday.
Sweden had appealed after the race but the International Triathlon Union (ITU) rejected it on Wednesday.
"The Swedish NOC and the STF consider that the ITU did not comply with its own rules because it may not have taken into account the position of the athletes' torsos when establishing the medal positions," said the court.
"They add that it is not possible to distinguish precisely on the photo-finish the position of Spirig's torso, which is slightly back from her belly and which is hidden by the torso of the Swedish athlete."
Spirig and Norden clocked identical times of one hour 59 minutes 48 seconds.
Judges examined the photographic evidence and decided Spirig's winning margin was less than 15 centimetres. Officials later issued a photograph which appeared to show Norden's head crossing the finish first.
However the ITU ruled that the winner was the athlete whose torso crossed the line first, and said two cameras at the finish showed the Swiss athlete's torso ahead of the Swede's.
It was the first time that an Olympic triathlon had been decided on a photo-finish.