The SFV's decision came two weeks after FIFA threatened to suspend Switzerland if Sion were not punished for fielding six players who were signed in the summer when the club was subject to a transfer ban.
Sion had also defied FIFA and UEFA statutes by taking their case to the civil courts, at one stage forcing UEFA president Michel Platini to give explanations to a Swiss prosecutor.
"This points deduction is to punish the illegal behaviour of FC Sion, also contrary to the statutes and rules, by illegitimately getting around the transfer ban imposed by FIFA and fielding non-eligible players," the SFV said in a statement.
FIFA's Executive Committee, meeting in Tokyo on December 17, had given the Switzerland a deadline of January 13 to follow its instructions or face a ban which would also result in FC Basel being expelled from the Champions League.
However, it stopped short of FIFA's demand that Sion be punished with 3-0 defeats, saying this would have resulted in other teams being awarded points, distorting the championship.
Sion then obtained an injunction at another court in the canton of Vaud, where UEFA's headquarters are based, ordering European football's governing body to reinstate them to the competition.
The case has caused acute embarrassment to Switzerland with other clubs admitting it has damaged the country's image in the sport.
Last week, the Swiss Players' Union angrily criticised FIFA's ultimatum, accusing football's governing body of playing "power games" at the expenses of the FC Basel players, who had nothing to do with the Sion case.
FIFPro, the world players' union, has also hit out at FIFA.
"We do not agree with the consequence that players of FC Basel, a totally different club, or national team players become the victims of the actions of FC Sion," said general sectary Theo van Seggelen.
