Does minoxidil cause wrinkles / dark circles by slowing down collagen production of the skin?

I have not seen a double blind study documenting wrinkle production or dark circles. The dark circles could have other etiology eg lack of sleep, or genetic...I would recommend bringing your concerns about your beard to an experienced transplant surgeon. Hair transplant is a great option for restoring beard.

Excellent question. First of all, I agree about NO research studies. Also, I am not aware of any approval of Minoxidil research studies by the FDA for beard hair growth. So, it is very difficult to give you a clear and valid answer. I will suggest you to see for evaluation to the doctor that recommended you the Minoxidil for the beard. Good luck. 

Minoxidil can have side effects and may cause wrinkles as well as dark circles for some individuals. Chances are, minoxidil side effects won’t happen to you. The general consensus on the cause of wrinkles and eye circles is based on the fact that minoxidil slows down collagen production in the skin.
Collagen keeps skin taught, bright, and plush. As we age, collagen production slows and it results in wrinkles, dark eye circles and other visible signs of aging. Using minoxidil products may potentially speed this process up, by contributing to the decrease of collagen production. The first side effect to typically observe is the darkening eye circles. This is because the skin under your eyes is the most thin.
I’d say that it is always safe to first consult your physician before starting any form of medication, including minoxidil. You never know how your body will respond to it because each person reacts differently depending on your personal health and circumstances.