The complaint by the royalist military that ousted the government of Thaksin's sister stemmed from an interview he gave to foreign media in 2015. Thaksin, 74, denies the accusations and has repeatedly pledged his loyalty to the crown.
The next hearing has been set for May 29 because the investigation into the complaint has not been completed, Prayut Phetkhun, the spokesperson for Thailand's attorney-general, told a press conference.
"The results of the investigation have not been completed in all dimensions," he said.
Thailand forbids criticism of its royalty with a lese-majeste law that is one of the world's strictest of its kind.
The billionaire, who was convicted of abuse of power and conflicts of interest, was released on parole in February after six months in detention.
He made a dramatic return to Thailand in 2023 from 15 years of self-imposed exile, during which he remained a central figure throughout repeated bouts of political upheaval.
The founder of the populist Pheu Thai party has seen his family's parties win all but one election since 2001, with three Shinawatra governments toppled by coups or court rulings.
Thaksin's return and relatively short detention fed speculation of a deal he struck with his bitter rivals in the conservative establishment and military, which he has long blamed for trying to stifle pro-Thaksin governments.
His allies have denied any such deal.
Pheu Thai leads the current government, with Thaksin's business ally Srettha Thavisin prime minister and daughter Paetongtarn Shinawatra the party chief.
Commentators anticipate he will seek to wield political influence from behind the scenes, raising the prospect of another confrontation with his powerful establishment rivals.
