It Can. Talk to your doctor. Certainly anxiety & stress can cause facial numbing but so can vitamin deficiencies, trigeminal nerve problems, transient ischemic attacks (mini-strokes), and a variety of other illnesses. Your symptom must be evaluated in the context of what is going on in your life plus a thorough physical exam.
Yes. Stress can causes many physical symptoms: headaches, stomach aches, back aches, skin rashes, itching, upset stomach, tight throat, muscle tension, jaw clenching, etc etc. Numbness is less common but certainly possible. Numbness and tingling around the mouth or in the fingers is especially characteristic of hyperventilation. See: http://en.Wikipedia.Org/wiki/hyperventilation_syndrome.
Stress & Face Numb. When you are under stress, adrenaline is released into the blood stream causing the heart to race and blood vessels to selectively supply muscles that help with the fight or flight response. Blood vessels of the face and head narrow and restrict nerve function, leading to facial numbness.