Is sclerotherapy safe on blue veins on the face? (Photo)

Treating larger veins on the face (temples, forehead, around eyes) with sclerotherapy is not a "common" procedure. However, I am using sclerotherapy on face veins in my practice, and find it to be 1. safe, and 2. effective. Make sure you go to a board certified, surgical/procedural MD with a lot of vein experience. And, make sure he/she has done facial veins. The procedure itself is pretty easy. I use hypertonic saline (better safety profile). It is tolerated, but can burn, and cause a sort of muscle ache while the solution is being injected. I believe that a pressure bandage for 12 to 24 hours after treatment is important. Finally, it will take more than one treatment. Space them at least 4 weeks apart. 

First the picture is of law quality. As to your question,  YES, it is if you are in good hands. As to the small red veins on the cheeks, the best is laser treatment. Injecting into an artery catastrophic as it can cause skin necrosis resulting in an ugly scar.

Sclerotherapy should work well on the posted veins in your pictures.  It is crucial to ensure that the structures are veins and not arteries (the pictures look like veins to me).  Injecting an artery can impede the blood supply to certain areas of the face (although this is  unusual to happen since the face is very vascular).

if your doctor is telling you they might be arteries, what they are telling you is that they are not sure and you should not have treatment with that particular doctor. We treat this area routinely, but that does not make it routine. The anatomy is complex and, in the wrong hands, complications may occur at higher rates. Go to someone who has experience treating facial veins. We have people travel from all over the west coast to our office for treatment of the most complex leg, facial, breast, and hand veins. Good luck.