King Vajiralongkorn quashed the candidacy the same day it was filed in a royal command calling it "highly inappropriate", prompting an immediate reversal from the party.
The Thai Raksa Chart party took an extraordinary political risk on Friday when it put forward Ubolratana as its candidate.
The court said it would decide on Thursday whether or not to accept the case.
The party on February 8 named Princess Ubolratana Mahidol its candidate for prime minister for a general election next month.
Ubolratana's bid was particularly notable because she allied herself with a party that is part of the political machine of former Prime Minister Thaksin Shinawatra, who was ousted in a 2006 military coup and is loathed by many royalists and others in the country's traditional establishment.
Junta leader Prayut Chan-O-Cha has agreed to stand for premier again under a military-aligned party.
In an Instagram post late Tuesday the 67-year-old princess apologized for her role in the drama.
"I am sorry my genuine intention to work for the country and Thai people has caused such problems that shouldn't have happened in this era", she said on Instagram after making a public appearance in central Thailand.
The future of the party that nominated her, Thai Raksa Chart, is now in doubt amid calls for it to be disbanded.
Last week, Thailand's election panel said it had excluded Princess Ubolratana because "every member of the royal family comes within the application of the same rule requiring the monarch to be above politics and to be politically neutral".
"We must wait for [the court's] process", he said. The constitutional court is expected to approve the election commission's request.
The court will make its decision based on an article in Thai law that forbids the "sabotage" of Thailand's constitutional monarchy, a system that since 1932 has made the monarch the head of state and the prime minister the head of government.
However, they could hope to run in the next election. Under the military-drafted constitution, the junta appoints all of the upper house, which along with the lower house gets to vote for prime minister.
Thai Princess Ubolratana Rajakanya poses during a news conference at the 61st Cannes Film Festival. They appear to have assumed that since she lost her formal royal titles in 1972 when she married a foreigner - an American whom she has since divorced - that the strictures against royal involvement in politics would not apply to her.
"We urge you to give Thai Raksa Chart a chance to object and show supporting evidence within a suitable period of time", he said. It would also deepen concerns about the fairness of the March 24 poll, the first since the coup.
Voice TV, owned by Thaksin's son Ponthongtae, was ordered Tuesday by the National Broadcasting and Telecommunications Commission (NBTC) to go off-air for 15 days after two of its programs caused "confusion and provocation".
Voice TV CEO Mekin Petplai said the move was unfair and "affects freedom of the press" in the run-up towards the election.