The 'I Will Always Love You' singer passed away on Saturday (February 11) at the age of 48 in her room at the Beverly Hilton.
Her sudden death sparked an outpouring of emotion similar to when Jackson suffered a fatal cardiac arrest at the age of 50 in June 2009.
The 'Billie Jean' singer's siblings Janet Jackson and Randy Jackson have since posted a message of condolence on their Twitter profiles, in which they request that Houston's family be granted "patience and comfort" as they come to terms with the tragedy.
"We honour and celebrate the life of one of the world's most gifted vocalists and talented entertainers, Whitney Houston," the Jackson family's statement reads.
"Although we are all saddened by her sudden passing and will miss her, we respectfully ask everyone to consider her family at this time of difficulty by granting them the patience and comfort they need to mourn their loss in peace."
Jermaine Jackson, meanwhile, left his own tribute on Twitter, writing: "The right words fail me to sum up the sense of loss following the passing of Whitney ... a wonderful woman, a true heart, and an immense artist.
"Now is not the time for anyone to indulge in negative speculation. It is a time to honour her talent and a voice which the world enjoyed. She is gone too soon, but that incredible voice will live on as an eternal reminder of her timeless talent. Rest in peace my friend."
Houston's official cause of death has not yet been released, as the results of an autopsy have been put on hold pending further tests.
Watch Whitney Houston perform 'I Will Always Love You' below: