With shooting guard Bradley Beal's playing time limited by injuries recently, and Neal sidelined the past 14 games with a bad leg, the Wizards wanted some backcourt depth.
The Wizards signed Neal as a free agent in July, hoping he could help offset the departure of Paul Pierce.
Neal averaged 9.8 points for Washington, but he appeared in only 40 of the team's 63 games entering Wednesday.
Thornton has played seven seasons with six NBA teams, averaging 12.4 points, 2.8 rebounds and 1.4 assists.
In 47 games with the Houston Rockets this season, Thornton averaged 10 points. Houston waived him last month.