The Mavs received a conditional second-round draft pick in 2012, while the Wolves also received cash.
Jawai was a contractual throw-in from Toronto in the four-team trade in July that brought Shawn Marion to the Mavericks and has been shopped since his arrival in Dallas.
The Mavericks were pessimistic about being able to find a new home for the burly Australian, even given Jawai's modest $736,420 salary, but injuries to Kevin Love and Al Jefferson have created a short-term need for size in Minnesota.
Love is out six to eight weeks with a broken hand and Jefferson -- who is recovering from a torn ACL suffered last season -- has been plagued by a sore Achilles tendon.
The Mavericks' roster now stands at 16 players, but they would need to either trade or buy out the $2.4 million expiring contract of exiled swingman Shawne Williams to make room for veteran Jake Voskuhl, whom Dallas would like to keep as a third center.
ESPN.com reported earlier this month that the Mavericks were also exploring the feasibility of suspending Williams for unspecified conduct detrimental to the team. Williams has continued to draw checks from the Mavericks even though he was sent home last season for what the club deemed to be consistently unprofessional conduct after appearing in just 15 games. But all suspensions in the NBA are without pay.
Like Jawai, Williams has been offered in trades for some time after the Mavs made a quick determination that last October's training-camp acquisition of the 23-year-old from Indiana and subsequent willingness to pick up Williams' option for this season were mistakes.
The conditional draft pick the Mavs get is protected through the 55th overall
Wolves president of basketball operations David Kahn says the team was
considering the Jawai trade before Love broke
Marc Stein is a senior NBA writer for ESPN.com. Information from The Associated Press was used in this report.