Nakhid, 51, had challenged his exclusion by FIFA's ad-hoc electoral committee barring him from the February 26 vote to replace Sepp Blatter as the head of world football's governing body.
Nakhid's candidacy was invalidated because he only received four valid nominations out of FIFA's 209-member national association and presidential candidates required five.
A CAS statement confirmed previous reports that one of Nakhid's supporting associations also gave backing to another candidate, "in violation of the applicable FIFA rules."
"As a consequence, those letters of support were disregarded, meaning that David Nakhid had not met the qualifying criterion of obtaining declarations of support from at least five member associations, and accordingly, his candidature could not be validated," the statement further said.
Five candidates have so far been approved for the race to succeed Blatter, who is serving a 90-day suspension over corruption allegations.
They include France's Jerome Champagne, Prince Ali bin Al Hussein of Jordan, South African business tycoon Tokyo Sexwale, Asia's football chief Sheikh Salman bin Ebrahim Al Khalifa and Gianni Infantino, who is Michel Platini's deputy at the European confederation (UEFA).
Platini is still hoping to enter the race but he has been barred to date while serving his own suspension by FIFA's ethics committee.
He may face a stiffer punishment, including a possible lifetime ban, when FIFA's ethics court issues a verdict in Platini's corruption case next week.