Yes, numbness is associated with anxiety. When you perceive a threat, the fight-or-flight response is activated, and a part of the brain, the amygdala, becomes overactive. The amygdala then sets off a cascade where the sympathetic nervous system is activated, and the adrenal glands are signalled to release adrenaline and cortisol, the stress-response hormones. To prepare for the threat, resources are diverted to the skeletal muscles from other body systems to respond with either fighting or fleeing. When you are anxious and you set-off the fight-or-flight response, blood is shunted from your skin to the skeletal muscles by the constriction of blood vessels in your skin- this can manifest as numbness of your body.
If you are hyperventilating (breathing too deeply or too rapidly) during your anxiety attack, you can also experience numbing and tingling sensations (pins and needles sensations) of your arms/hands and legs/feet. What happens during hyperventilation is that while you are getting enough oxygen, you are blowing off a lot of carbon dioxide (CO2). This leads to low blood levels of CO2, and leads to constriction of the blood vessels, further leading to numbness. Soon, so much CO2 is blown off from the hyperventilation that respiratory alkalosis occurs, and this can result in paresthesias, or tingling sensations.
The best way to deal with the numbness is to address the underlying anxiety. If you also have hyperventilation, you will benefit from doing breathing exercises and relaxation techniques.