Wellbutrin® (bupropion hydrochloride). Between 1 in 100 and 1 in 1,000 people experience hair loss from Wellbutrin. If hair loss becomes a problem while taking Wellbutrin, talk with your healthcare provider. Depending on the severity of the hair loss, there are things that he or she may be able to do. It is possible that if hair loss is bothersome to you, your doctor may recommend adjusting the Wellbutrin dosage or may suggest trying another medicine for your condition.