The court is based in the canton of Valais, where Sion is located, while European football's governing body UEFA is based in the canton of Vaud.
Sion were kicked out of the Europa League on Friday after UEFA ruled they had fielded ineligible players in a play-off against Celtic, who took their place.
Sion had beaten the Scottish club 3-1 on aggregate in the two-leg tie.
"The judge declared... the requests for provisional and super-provisional measures to be inadmissible," said a statement issued on Valais canton's official website.
"In effect, according to applicable legislation, the litigation does not present a close enough connection with the canton of Valais to fall within the administration of the Valais judicial authorities."
"The measures requested by the complainant are aimed exclusively at UEFA, whose headquarters is in Nyon [in Vaud], and organisation of the Europa League."
Sion signed six players during the summer despite FIFA saying that the club was subject to a transfer ban, imposed after it was found guilty of inducing an Egyptian player to join the them while he was still under contract to another club.
Sion were initially banned from fielding the players in the Swiss League which reversed the decision after the players took their case to a civil court which ruled in their favour.
Sion then fielded some of them in the Europa League tie against Celtic.
FIFA statutes ban clubs and federations from taking sporting cases to civil courts and the Switzerland has been warned that it is expected to comply with this ruling.
However, the Swiss League has said it cannot defy a local court.
A UEFA spokesman said the governing body had so far not received any appeal from Sion, who said last week that they planned to do so.
