Is there a procedure to remove a blue vein under my eye?
Yes, there is but it could be a bit dangerous. Deep blue veins are often best treated with sclerotherapy. The vein is cannulated and a sclerosing solution is injected causing the vein to clot. Slowly with time these veins dissipate. Unfortunately, many of the veins around the eye communicate back to the retina with few valves to stop the sclerosing solution from going to your retina. If the retina is sclerosed, you could go blind in that eye. There are techniques to assist in preventing this event from occurring but, it is most likely a risk you would have to be willing to take to address/correct your concern.
Laser technology continues to advance quite rapidly, so hopefully in the future there will be better techniques to correct the deep blue veins around a patients eyes.
Gary R Culbertson, MD, FACS