Having been asked this question, I was only aware of the fact that premature epiphysis closure is a side effect of isotretinoin therapy in children (Tran 2008).
While DELAYED epiphysis closure is known for rickets, it is an interesting question if vitamin D supplements given to adolescents will be leading to a premature end of longitudinal growth. Maybe this is also a difficult question as the answer will depend on long-time vitamin D, calcium and phosphate status; it will depend on dose and application scheme of any vitamin D supplement. And it will depend to some extent on the genetically determined vitamin D hydroxylase activity. The ultimate textbook (Feldman, Vitamin D, p864) writes
With treatment the unmineralized osteoid of the growth plate of the metaphysics ad epiphysis will mineralize.
This is in line with original research in rats (Boris 1978) showing
The results … indicate that the administration of la,25-(OH)2-D3 during the recovery period after EHDP administration significantly improved the uptake of 5Ca by the epiphyseal plate while reducing the plate width.
and probably also in calves ( Woddard 1997 ) although that study also included vitamin A.
This study showed that vitamin A induced growth-plate closure if calves were given an intramuscular injection of vitamins A and D (2,000,000 IU and 300,000 IU, respectively) on the first day after birth
So we need to ask first if an adolescent gets additional vitamin A for acne treatment. For vitamin D supplementation, the case is rather unlikely at the moment.. The only intervention study that I know of (Morandi 2014) missed some important aspects by focusing only on “growing pain”. As we now have the possibility of doing PET scans of the epiphysis, it would be a good research question to be safe with vitamin Du supplementation of adolescents.