Bach told a press conference that the International Olympic Committee's ethics committee would not decide whether to take action until the criminal procedure against the 71-year-old Hickey is completed.
Hickey, the head of the Olympic Council of Ireland and the European Olympic Committees, was detained Wednesday and is accused of involvement in a ticket scam, ambush marketing and conspiracy over the sale of Rio Olympics tickets at inflated prices.
"What we know is that he has not yet been heard by a judge," Bach told a press conference on the sidelines of the Rio Olympics.
He said the IOC ethics commission "is in contact ... With the authorities here in Brazil."
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But as Hickey has voluntarily stood down "temporarily" from his posts, the commission can do no more "and will follow up the case according to the developments with regard to the legal procedure."
"We respect the laws and legal procedures in Brazil and I cannot comment further at this moment," Bach said.
Police said they seized hundreds of tickets from Mallon some of which had the Olympic Council of Ireland name on them.
Tickets, including for the Rio opening ceremony, with a face value of about $1,400 dollars were offered for sale at $8,000.
Hickey denied any involvement with THG before his arrest.