Blood vessels repair themselves after injury or trauma. How quickly this happens depends upon the general state of health of the person, other injuries sustained, and the existence of other diseases that delay healing.
In a relatively healthy person that sustained no other trauma to the tissues and who was not a diabetic, an average size vein will repair itself in just a couple of days. If the vein was a larger one, it may take a week or more. If the person is diabetic, healing may take months, and if the blood sugar is poorly controlled, the vein may never heal. When a diabetic has any wound to any area of the body, infection is always a concern because they are more prone to infections that do not heal because of the high concentration of blood glucose.