By waiving Curry, the Mavs remain at the 15-man roster limit.
With Chris Kaman soon to return from a calf injury, Dallas decided it needed more of a stretch power forward such as Murphy as cover for Dirk Nowitzki than another back-to-the-basket player such as Curry, sources told ESPN.com's Marc Stein.
In two games, Curry averaged 4.5 points and 2.0 rebounds in 12.5 minutes.
The 6-foot-11, 245-pound Murphy, a 12-year veteran, has career averages of 10.9 points and 7.9 rebounds per game. However, he's been a rarely used bench player the past three seasons for the then-New Jersey Nets, Boston Celtics and Los Angeles Lakers.
With Nowitzki out at least another two weeks while recovering from arthroscopic knee surgery, Murphy could provide the Mavs a perimeter shooting threat at power forward. He is a 39 percent career 3-point shooter.
Murphy, 32, has experience in Dallas coach Rick Carlisle's offense. He played for Carlisle with the Indiana Pacers in 2006-07, averaging 11.1 points and 6.1 rebounds after arriving in a midseason trade from the Golden State Warriors.
Information from The Associated Press was used in this report.