The English Premier League leaders had asked the Lausanne-based court for a stay until the result of an appeal was decided.
The CAS said in a statement that it had granted the request, with the sanctions suspended "until the CAS renders its final decision in this matter".
'TOTALLY DISPROPORTIONATE'
The English club, who have slammed the FIFA ban as "extraordinarily arbitrary" and "totally disproportionate", noted the CAS action on their website without further comment.
Manager Carlo Ancelotti batted off reporters' questions, saying Chelsea were concentrating on Sunday's home game against Manchester United and that the CAS situation would take care of itself.
"This means that Chelsea are free, if they wish to do so, to deal in the transfer market in January," he said.
"The key question now is when will CAS hear the appeal and finally decide?
"Under the CAS procedural rules, generally speaking an appeal must be decided within four months of the pleadings having been settled, the pleadings being the statement of appeal, the answer to the appeal, any submission made in the case by the FIFA dispute resolution chamber.
"I don't think we will get an appeal much before March or even April of next year."
