The opposition Republican People's Party's (CHP) has repeatedly criticized the decision by the country's top election authority to accept ballot documents in envelopes without an official stamp.
The party formally lodged on Friday a petition with the Council of State, Turkey's highest administrative court, after the 'Yes' side won 51.4 percent of the vote on April 16.
The opposition argues the decision by the Supreme Election Board (YSK) on the envelopes opened the way for fraud, and launched a failed bid to annul the referendum last week.
The CHP argued the decision by the YSK was an "administrative" move.
However, the court rejected its challenge by majority vote, saying it could not rule on the YSK's move because it was "not an administrative procedure", state-run news agency Anadolu reported, according to AFP.
Turkish Justice Minister Bekir Bozdag said on Saturday that decisions made by the YSK could neither be challenged in the Constitutional Court nor the Council of State.
Levent Gok, CHP's parliamentary group leader, immediately hit back, accusing Bozdag of giving "instructions" to the judges before they had made a decision.
Turkey will implement an executive presidency from November 2019, axing the role of prime minister and empowering the president to appoint ministers.