U.S. authorities have opened a new front in their investigation into bitcoin exchanges and other businesses that deal in the online currency, examining possible ties between the firms and the online drug bazaar Silk Road, according to people familiar with the matter.

The new focus of the investigation is the latest indication of how the shuttered online drug market has become linked to bitcoin, tainting the currency with associations of shady activity as its advocates stress to regulators its legitimacy. It comes after prosecutors...