Hudson's mother, brother and 7-year-old nephew were shot and killed in Chicago. Her sister's estranged husband has been called a person of interest in the triple homicide and is being held on an alleged parole violation. He has not been charged with the slayings.
"I want to thank each and every one of you for your thoughts and prayers during this difficult time. My sister and I take great comfort and strength from your love and concern," Hudson wrote in a message dated Thursday, Usmagazine reported.
Hudson, who won an Oscar for her work in the movie musical "Dreamgirls," has been keeping a low profile as she grieves for her dead family members.
E! News said the "Secret Life of Bees" star will still be featured as planned in Gap's new holiday ad campaign. The photos showing Hudson smiling and wearing a bright red sweater were taken in July.
Gap reportedly gave Hudson the chance to back out of the campaign out of consideration for the ordeal she is going through, but Hudson told the clothing chain to go ahead.
"She said she wanted to be a part of it and that we should move forward," E! quoted Gap spokeswoman Olive Doyne as saying.
Celebrity Families of 2014 [PHOTOS]