Supreme Court Justice Luis Roberto Barroso ruled there is sufficient evidence to investigate whether Temer signed a decree in May 2017 to favour a company operating in the port of Santos in exchange for bribes.
Barroso also authorised an investigation of Rodrigo Rocha Loures, a former Temer aide accused of carrying bribe money for Brazil's leader in a separate case.
Temer said in a statement that he "had no interference in the debate" which led to the decree and that he "accepted the deliberations and technical advice, without any kind of political pressure staining the whole process".
Brazil's top prosecutor, Rodrigo Janot, whose attempt earlier this year to put Temer on trial for a corruption charge was rejected by Congress' lower house, will lead the new investigation until his term ends on Sunday.
Raquel Dodge, an appointee of the president, will take over as chief prosecutor on Monday. There is no deadline for the top prosecutor to decide on the case.
If Temer should be formally accused by Janot or Dodge, Congress would have to vote again on whether the president should be put on trial. If two-thirds of deputies agreed, Temer would be suspended for up to six months and the leader of the Chamber of Deputies would fill the presidency until the end of the trial.
A 'reasonable' investigation
Barroso said in his decision that the authorisation for investigation did not mean Temer was guilty, but the justice called evidence against the president "plausible" and the request to investigate him "reasonable".
"No one should be indifferent to the personal and political onus for a public authority, notably the president, in appearing as investigated in a procedure of this nature. But that is the price imposed by republican principles," Barroso wrote.
Janot formally accused Temer of corruption and money laundering in July, but the Chamber of Deputies decided not to suspend the president for allegedly being paid bribes by executives of JBS, a big meatpacking company.
On Monday, two executives of that company were arrested for allegedly hiding evidence from prosecutors.
Politicians expect Janot to come forward later this week with a new charge against Temer, this time alleging obstruction of justice and being member of a criminal organisation. That investigation was authorised by Supreme Court Justice Luiz Edson Fachin earlier this year.