General manager Daryl Morey said Sunday that the team will continue to work with White in hopes of finding a resolution.
White will not be paid during his suspension.
White refused his assignment to Houston's D-League affiliate a week ago. The 16th overall pick in the June draft has spent most of the season on Houston's inactive list while he and the team figure out how to handle his anxiety disorder and overall mental health.
White has been vocal on Twitter throughout this saga, and he continued to voice his opinions on the website after the announcement Sunday.
"What's suspending me suppose to do. I've been away from the team for a month ½. Guess we want to give it a title to shift accountability," he tweeted.
That was the first in a string of tweets on the subject, and he then addressed Morey in the second one.
"Threat, Fines, Suspension won't deter me. I won't accept illogical health decisions, I will keep asking for safety & health. #BeWell @dmorey," he tweeted.
The Rockets chose White in the first round after a season at Iowa State, where he helped the Cyclones to their first NCAA tournament berth in seven years by leading the team in scoring (13.4 points a game), rebounds (9.3), assists (5.0), steals (1.2) and blocks (0.9).
The 6-foot-8 White missed the first week of training camp to work with the Rockets to create an arrangement to deal with his anxiety disorder within the demands of the NBA's travel schedule. He and the team agreed to allow him to travel by bus to some games while he confronted his fear of flying and obsessive-compulsive disorder. He flew to Detroit with the team for the season opener and then traveled by bus to Atlanta and Memphis for games.
But he soon stopped participating in team activities and said on Twitter that dealing with his mental health took precedence over his NBA career. Then came his decision last Sunday to refuse his assignment to the D-League. Despite that decision, he said then that he still hopes to return to basketball in the future.
"And daily I'm just trying to stand up for my health and make sure that my health isn't neglected in an operation where, me and you both know, it's mostly about money," White said in a recent interview with Sirius/XM Radio. "And I'm kind of the only one that's going to sit in the situation and say, 'Hey, let's put the health thing first.' "