Does skin necrosis require immediate surgery?

Yes, it may: You should be evaluated immediately, hopefully, the skin can be saved!

Depends: Necrosis comes in two varieties, wet and dry. Dry necrosis black, plaque adheres to the wound. Wet necrosis is red, swollen, spreads quickly, painful and very dangerous. It might start at a skin lesion, or at dry necrosis site but can spread into deeper tissues. Wet necrosis, aka necrotizing fascitis, or gangrene requires immediate surgery and very aggressive medical therapy.