The draft pick the Hawks are receiving is lottery-protected from 2017-20, reports Brian Windhorst of ESPN.
The Hawks selected Payne out of Michigan State with the No. 15 pick in last June's draft. He has appeared in just three games this season, posting five minutes and four rebounds. Payne spent four stints in the NBA Development League, including two each with the Fort Wayne Mad Ants and Austin Spurs.
The trade opens up a roster spot for the Hawks. Last week, Vivlamore reported the team had held talks with free-agent shooting guard Ray Allen, though at the time, nothing was "imminent." Allen will reportedly make a decision about his NBA future shortly after All-Star weekend.
The Hawks currently hold the NBA's second-best record at 43-10 and lead the Eastern Conference by 7.5 games over the Toronto Raptors.
The Timberwolves are 11-41, the worst record in the Western Conference.
- Mike Fiammetta