The decision comes after three ministers quit in recent weeks as the government battles to jumpstart an underperforming economy and find funds to deliver on a delayed election promise of cash handouts for 50 million people.
The court chose not to suspend Srettha from duty pending a verdict, as was sought by 40 senators who had complained Pichit Chuenban fell short of moral and ethical standards for ministers set out in the constitution.
Srettha has 15 days to file his defence in court.
"The prime minister is focused and determined, this will not affect his work," said government spokesperson Chai Wacharonke.
Pichit's qualifications prior to becoming a minister in the prime minister's office had been carefully vetted and the appointment was in line with the law, he added.
For decades a close aide of the politically influential Shinawatra family, Pichit resigned on Tuesday in an effort to insulate Srettha from the court case.
He had been jailed for six months in 2008 for contempt of court after being accused of a bid to bribe court officials with 2 million baht ($55,218) placed in a grocery paper bag, which he denied. His law license was suspended for five years.
INFLUENTIAL CLIENTS
As a lawyer, Pichit fought, and lost, big court cases against former premiers Yingluck Shinawatra and billionaire Thaksin Shinawatra, who has been a towering figure in Thailand for more than two decades.
Thaksin is a close ally of Srettha and founder of his ruling Pheu Thai party, which together with its predecessors has won all but one Thai election since 2001.
The court gave no timeframe for a decision in the case.
If it dismisses Srettha, a new government must be formed and Pheu Thai would need to put forward a new candidate for premier to be voted on by a parliament in which it is not the biggest party.
Real estate mogul Srettha was elected by the legislature in August last year after weeks of political deadlock, following a deal with parties and lawmakers allied with the royalist military, which staged coups against Shinawatra-backed governments in 2006 and 2014.
Government critics say Pichit got the job thanks to his close ties with Thaksin. The tycoon still holds significant sway in politics, despite officially being retired and having spent 15 years in self-imposed exile until his return last year.
The government has said Pichit was picked because he was suitable.
Thaksin, who was convicted of conflicts of interest and abuse of power and was released from detention on parole in February, will learn next week if he is to be prosecuted for an alleged insult to the powerful monarchy.
He has denied wrongdoing in the case over comments made in an interview a decade ago.
