Nick and Aaron Carter's sister, Bobbie Jean Carter, has died ... TMZ has learned.

Bobbie Jean's mother, Jane Carter, tells us ... "I am in shock from learning of the sudden death of my daughter, Bobbie Jean; and I will need time to process the terrible reality of this happening for the third time.  When I am able to think clearly, I’ll release a fuller statement; but until then I would request to be left to grieve in private."

She adds ... "[H]owever deeply a parent feels the loss of a child, the suffering of a young child at the loss of a parent must be much greater. So, I would ask the sympathetic to say a prayer for my precious eight year old granddaughter Bella, who previously lost her father and is now also left without her mother."

The exact circumstances of Bobbie's death are unclear, but we know she passed away Saturday morning in Florida.

Bobbie Jean -- otherwise known as BJ -- was somewhat involved in the family's music business during the height of her brothers' careers ... especially Aaron, for whom she served as a wardrobe stylist and makeup artist during his tours back in the early 2000s.

She also appeared on the family's E! reality TV show, "House of Carters," on which she was featured in eight episodes. In the years since, Bobbie Jean lived a relatively private life in obscurity, shying away from the spotlight.

Bobbie Jean suffered from addiction and substance abuse over the years ... something that was documented on TV, and which she continued to battle into her later years of adulthood.

She had legal troubles as well, with arrests documented as recently as this year.

BJ's death marks yet another tragedy for the family at large. Not only did they lose Aaron last year due to a drowning at his home -- which was also found to have been drug-related -- but the Carters also lost their other sister, Leslie, in 2012 ... as a result of an overdose.

Now, the only living Carter siblings are Nick and Angel ... there are half-siblings and step-siblings in the family as well. Bobbie Jean is survived by a young daughter, Bella.

Bobbie Jean was 41.

RIP