WASHINGTON—The Justice Department said Tuesday it seized over $3.6 billion worth of digital currency stolen during a hack of a cryptocurrency exchange and arrested two suspects for allegedly trying to launder the proceeds.

The value of the cryptocurrency at the time it was seized last week marks the largest financial seizure ever by the Justice Department, officials said.

Ilya Lichtenstein, 34 years old, and his wife, Heather Morgan, 31, were both arrested without incident Tuesday morning in Manhattan, the department said. They have promoted themselves on social media as entrepreneurs with deep knowledge of tech and a love of travel.