SÃO PAULO, Brazil — The presiding judge on Brazil’s Supreme Court overturned an injunction on Friday that had suspended an investigation into bank transactions involving Flávio Bolsonaro, the eldest son of President Jair Bolsonaro, ruling that the inquiry could proceed.

The investigation has proved one of the biggest challenges to Mr. Bolsonaro, a far-right politician who rose to power in Brazil on the back of his promise to eradicate entrenched political corruption and elitist privileges.

The case involving Flávio Bolsonaro began unfolding in December, when federal financial investigators discovered that about 1.2 million reais, or about $327,000, had been moved in and out of a bank account belonging to an aide, Fabrício Queiroz, in 2017. At the time, Flávio Bolsonaro was a Rio de Janeiro State lawmaker and Mr. Queiroz was his driver.

Some of the payments were to Michelle Bolsonaro, the wife of the current president. Jair Bolsonaro has said that those transactions were because Mr. Queiroz was repaying a loan to his wife.