Beverley will undergo further evaluation in seven to 10 days and could need season-ending surgery, the report says.
He has been ruled out for Wednesday's game against the New Orleans Pelicans.
The 26-year-old was taken to Houston on Tuesday to have the wrist evaluated and met with doctors on Wednesday, Wojnarowski reported.
From the report:
Beverley met with doctors on Wednesday in Houston, where it was determined that more time was needed to evaluate the extent of the injury and the potential for further damage if he continues to play with it this season.
Beverley is in his third season with the Rockets since being selected in the second round of the 2009 draft out of Arkansas.
Over 56 games (and 55 starts) this season, he has averaged 10.1 points, 4.2 rebounds, 3.4 assists and 1.1 steals.
An All-Defensive Second Team member last season, Beverley is set to enter unrestricted free agency this summer.