Sion, deducted 36 points this season in a legal row, and financially-troubled Servette Geneva were also turned down in the first instance as the league got tough following a year which saw Neuchatel Xamax kicked out of the championship.
The clubs have five days in which to appeal. Seven second division clubs also had applications refused.
"For reasons of infrastructure and finance, the Swiss Football League's licensing department has not granted the request for four Super League clubs," the league said in a statement.
"The commission has applied strict criteria, due to the experience of the past seasons. The budgets for the 2012/13 season have been examined from every angle."
FC Zurich have been Swiss champions 12 times and twice reached the semi-finals of the old European Cup while Young Boys have won the domestic title 11 times and reached the European Cup semi-finals in 1959.
Young Boys, coached by former Tottenham Hotspur manager Christian Gross, are third this term which would earn them a place in the Europa League qualifying rounds.
"In most cases, the refusals are due mainly for failing to meet financial criteria," said the league's statement, without going into further detail.
Switzerland, famous for its organisation, is the home of world governing body FIFA and European equivalent UEFA but its domestic football has endured a chaotic year with the problems centered around Sion and Neuchatel Xamax.
Sion were deducted 36 points for fielding ineligible players who they had signed during the close season while being subject to a transfer ban.
The case took on international dimensions when they fielded some of the players in a Europe League qualifying match and were thrown out of the competition.
The club then defied UEFA and FIFA statutes by taking their case to the Swiss civil courts, prompting the threat of an international ban for the country's football federation.
Neuchatel Xamax were expelled from the league in January over a number of irregularities including the suspicion that Russian-born owner Bulat Chagaev had forged a letter from a bank which he used as proof of his financial situation.
Chagaev, subsequently arrested and placed in custody on charges of financial mismanagement, had only taken over the club eight months earlier.
In that time, he fired four coaches, the club's administrative staff and terminated all sponsorship contracts.
Seventeen-times Swiss champions Servette filed for bankruptcy on March 1.
Since then the club has been sold to Canadian businessman Hugh Quennec, who is desperately trying to raise enough cash to keep the club afloat.
There was more confusion on Sunday when FC Basel effectively won this season's championship but refused to celebrate.
Basel took an unassailable 16-point lead over FC Luzer
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