Mother-of-one Leslie Carter passed away on Tuesday (January 31) at the age of 25. A cause of death has yet to be released.
In the wake of the tragedy, 24-year-old Aaron has taken to Twitter and thanked fans for the "love and prayers" sent to his family.
"My 'Family' Appreciates your love and prayers," he wrote. "My Father (Bob Carter) My mother (Jane) (Angel) (Bobbie Jean) & her husband (Mike Ashton)."
He went on to post a series of hashtags reflecting on his sister's death: "#broken #distraught #pain #confusion #disbelief #agony #Anger #lost #Sad #Family #LeslieCarter #empty #Leslie #dazed #Heaven #Sister."
It has been confirmed that Aaron will take leave from his role in a Broadway production of The Fantasticks.
"Aaron is taking a few days off from the show," a spokesperson told E!. "His Fantasticks family loves him and offers him support and prayers during this difficult time. We thank everyone for the outpouring of concern for Aaron."
Backstreet Boys star Nick has also paid tribute to his sibling online, announcing on Facebook that the band's joint tour with New Kids On The Block will be dedicated to Leslie.
A post on his official profile read: "Nick Carter is thankful to the many people and the fans who have shared their wishes and prayers during this tragic time. We want to let the fans know the tour will go on as promised."
The message finishes with a quote from Nick explaining: "Performing is cathartic to me and I am dedicating the rest of my tour to my sister since she loved to watch me perform."
The Backstreet Boys/New Kids On The Block jaunt will recommence in Belfast on April 20. They will also visit the UK, Australia and several European countries before their final date in Indonesia on June 1.
A statement released by the Carters yesterday (February 1) read: "Our family is grieving right now and it's a private matter. We are deeply saddened for the loss of our beloved sister, daughter and granddaughter Leslie Carter. We request the utmost privacy during this difficult time."