The court said the changes contradicted existing laws and "deviated from the objective of resolving problems" in the education system, Anatolia reported.
It will now decide whether to scrap the regulation altogether.
Education is one of the main battlefields for Turkey's secularists and the ruling Justice and Development Party (AKP), the moderate offshoot of a now-banned Islamist movement, which opponents accuse of seeking to raise the profile of Islam in Turkey and undermine the secular system.
Turkey's government-run religious high schools are tasked by law to educate preachers and other Muslim clergy, but many regard them as a breeding ground for Islamist political movements.
The notoriously complicated university entrance system had so far made it extremely difficult for graduates of such schools to gain a place at higher education institutions other than divinity faculties.
The measure had been designed to effectively block Islamist-leaning Turks from obtaining university degrees essential to holding top public service jobs.
The blocked regulation would have removed that barrier by scrapping arrangements setting different criteria at university entrance exams for graduates from different schools.
Prime Minister Recep Tayyip Erdogan, himself a graduate of an Islamic high school, had welcomed the changes, saying they "remedied an injustice against freedom of education."
Last year, the Constitutional Court scrapped an AKP-sponsored law that would have allowed students to wear the Islamic headscarf in universities.
Shortly afterwards, the AKP itself narrowly escaped being banned by the same court for breaching Turkey's secular principles.
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