Justice Celso de Mello gave the federal police 60 days to carry out the investigation requested by Brazil's chief public prosecutor Augusto Aras following the accusations made by former justice minister Sergio Moro, who resigned on Friday.
Moro said Bolsonaro had pressed him to change the chief of the federal police and accused the president of seeking to interfere in investigations that involved family members, to the point of requesting intelligence files.
Bolsonaro called the accusations unfounded, but they have set off the worst political crisis since he took office in January last year and lost the far-right leader valuable allies.
The investigation comes at a bad moment for Bolsonaro who is facing criticism for downplaying the gravity of the coronavirus epidemic that has killed over 4,500 people in the country and virtually paralyzed Latin America's largest economy.
Based on the results of the police investigation, the public prosecutor will have to decide whether to press charges against the president or his former minister.
An indictment of the president would have to be approved by the lower house of Congress before a trial could move ahead in the Supreme Court. The house is however dominated by Bolsonaro's supporters and it is unlikely to approve an indictment.
If he is indicted, the president would be suspended and Vice President Hamilton Mourao takes over his position temporarily for up to 180 days. If convicted in a trial, he would lose office.A poll conducted on Monday showed that a majority of Brazilians believe Moro's accusations are true. Forty six percent believe Bolsonaro should resign, while 50% who think he should not.