Mnuchin pledged to work with other governments, including within the Group of 20, which includes the world's major economies, to monitor the activity of those who invest heavily in the cryptocurrency.
"One of the things we will be working with the G20 on is making sure that this doesn't become the Swiss numbered bank account," he said at a conference, referring to the famously secretive accounts used by some to hide ill-gotten gains.
"We want make sure that bad people can't use this currency to do bad things."
US rule require banks to have information on customers with bitcoin accounts to try to prevent money laundering and other illicit activity.
Mnuchin acknowledged that some central banks were looking into the possibility of creating digital currencies instead of issuing cash, but said the US Federal Reserve was not yet considering such a move.
Asked about the possibility that Russia would create its own virtual currency to escape financial sanctions, Mnuchin said "I don't think that's a concern."