FIFA had threatened to expel the body and all member clubs unless they took sanctions against Sion before January 13th.
The ASF said it was complying with the world football governing body's demand by deducting 36 points after the club fielded at least one of six non-eligible players in a total of 12 matches -- 10 Axpo Super League games and two Swiss Cup matches.
"This points deduction punishes the breach of rules by FC Sion ... in respect of its illegitimate by-passing of a transfer ban imposed by FIFA and fielding potentially non-eligible players," the body said in a statement.
The ASF said it had asked FIFA on Thursday to confirm that the ban would not come into force following its action but it had not had a response.
A statement issued by FIFA said it had taken note of the decision.
"FIFA will now analyse the documents and submit them to the emergency committee in early January for a decision," it said.
The decision puts FC Sion at the bottom of the Super League with minus five points but the club could continue in the Swiss Cup.
The row erupted after the club, the subject of a FIFA-imposed transfer embargo over the signing of Egyptian goalkeeper Essam El Hadary, proceeded to sign six players in the summer.
The club then fielded five of the six players during a Europa League play-off tie against Celtic earlier this year and were kicked out of the competition.
UEFA's decision to expel them was later upheld by the Court of Arbitration for Sport.
Sion announced on Thursday it had launched a legal action in Zurich against FIFA, accusing the body of "unacceptable blackmail" for attempting to force the ASF to take action that would "run contrary to their own rules and to Swiss law".