Kim entered an undisclosed medical facility last week to get help for an alleged substance abuse problem.
Her co-star Taylor Armstrong suggested in a subsequent television interview that the rehab stint will inspire Kim to get her life back on track.
"I adore Kim and I stand behind her," Armstrong said at the time.
Kim's sister Kyle has now spoken openly about her sibling's struggle with substance abuse for the first time, telling Us Weekly that Kim is getting the support that she needs.
"[Kim is] doing very well. Fantastic," Kyle told the magazine.
The sisters, who are Paris Hilton's aunts, famously argued over Kim's alleged drinking problem during an episode of The Real Housewives of Beverly Hills, but later made peace.
It is not yet known how long Kim will be staying in rehab.
The Real Housewives of Beverly Hills airs Mondays at 9/8c on Bravo.
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Watch Kim Richards in a clip from The Real Housewives of Beverly Hills below (US only):