The Swiss club were put under a transfer embargo over the signing of Egyptian goalkeeper Essam El Hadary, but proceeded to sign six players in the summer.
Sion then fielded five of the six players during the Europa League play-off tie against Celtic earlier this year and were kicked out of the competition as a result, with UEFA's decision to expel them upheld by the Court of Arbitration for Sport earlier this week.
FIFA have now ordered the Swiss Football Association to sanction Sion or risk Switzerland being excluded from all football - which would mean Basel missing out on taking part in the Champions League last 16 and the national team missing out on an encounter with Argentina in February.
This could potentially see Manchester United, who are preparing for a Europa League campaign, back in the Champions League to face Basel's opponents Bayern Munich in the round of 16.
A statement from FIFA read: "The executive decided to give a final deadline of 13 January 2012 to the Swiss FA to enforce the registration ban imposed on Sion by the FIFA Dispute Resolution Chamber and confirmed by the Swiss Federal Court and to sanction the attitude of the club repeatedly trying to circumvent this decision in a legally abusive manner.
"As a consequence, all matches in which the relevant players participated shall be declared forfeit or three points shall be deducted respectively. Should this deadline not be respected, the Swiss FA will be automatically suspended from 14 January 2012 onwards."