Wright is not expected to undergo surgery, but he will be sidelined indefinitely. A source said he's expected to be in a sling for about 10 days before being re-evaluated.
Wright, whom the Mavs are counting on to play a key reserve role, injured the shoulder during Tuesday's practice and did not play in Wednesday's preseason win against the Memphis Grizzlies.
Wright, who signed a two-year, $10 million deal to return to Dallas after a strong finish to last season, has a history of problems with that shoulder.
The 6-foot-10 Wright injured the shoulder multiple times during his stint with the Golden State Warriors, for whom he played in 98 games over parts of four seasons after being selected with the eighth overall pick in the 2007 draft. He missed the 2009-10 season after undergoing surgery on the shoulder.