"We either would have to do something we're not comfortable with or leave New York," ShapeShift CEO Erik Voorhees told CNBC. "It's a moral and ethical stand we're going take."
The BitLicense—drafted by the office of Benjamin Lawsky, New York's outgoing superintendent of financial services—seeks to provide consumer protection for digital currencies. But it also moves to institute provisions like "know your customer," which authorities say are important to prevent fraud, money laundering and funding for terrorism.
Read MoreNew York regulator issues final bitcoin rules
Voorhees, however, said these goals do not justify the risk of exposing customers to a potential data breach—after all, he said, major companies and governments have proven unable to secure their data from hackers.
"We're not going to spy on thousands of people purely to make their job a little bit easier," Voorhees said of law enforcement, challenging the practice of opening up customers to potential identify theft simply to prevent drug money from "circling around."
The New York Department of Financial Services anticipated some responses like ShapeShift's, according to a spokesman for the department.
"We always recognized that there is going to be some part of this community that is against even pretty standard financial regulatory oversight measures, such as anti-money laundering controls and other consumer protections," he said in a statement to CNBC. "That said, one digital currency company has already received a license from NYDFS and a number of others have stated they intend to seek BitLicenses shortly."
Read MoreWhy financial firms are investigating bitcoin tech
"Ultimately, we believe that prudent regulation will be important to building greater consumer confidence in digital currency and sparking wider adoption," the spokesman added.
If authorities went through the proper channels to collect information from ShapeShift, Voorhees said, then he would be willing to provide wallet addresses, IP logs and information on what devices were used to access the platform—but not names and addresses.
All attempts at using ShapeShift within New York will redirect to PleaseProtectConsumers.org, Voorhees said, adding that he expects to sacrifice about 1 percent of volume on the decision.
Others in the bitcoin world have also criticized the notion of applying "know your customer" regulations to digital currency.
CORRECTION: This story has been updated to show the correct web address is PleaseProtectConsumers.org.