Authorities say 27-year-old William Balfour was arrested Monday at a prison where he was being held on a parole violation.
Chicago police spokeswoman Monique Bond says Balfour has been released to detectives and is awaiting formal charges.
The bodies of Hudson's mother, Darnell Hudson Donerson, and brother, Jason Hudson, were discovered in October at the family home in Chicago.
The body of the singer's nephew Julian King was found three days later in a vehicle on the city's West Side.
Police took Balfour into custody the same day the adults' bodies were discovered.
Slideshow archive | Local events | Contests | Headlines at a glance