You can try taking this up with people higher up in the hierarchy as others have suggested but in my experience that usually leads to no meaningful results. After decades of working in many different companies in several industries I have realized that corporations are breeding grounds for all forms of mental disorders (especially ego disorders like narcissism) much like septic tanks are breeding grounds for bacteria. The higher you go in a corporate hierarchy the more are the chances of encountering people with mental disorders, especially at the C-level. That is why taking up such problems with the supervisor may not yield anything meaningful.
The most effective way that I have found handling such narcissistic co-workers is to do unto them as they do unto you. Rather than tackle the morale problem, confront the cause of the morale problem - the narcissist himself. For example, always refer to the narcissist within his earshot as "genius" in an obviously sarcastic and sneering way. When he makes a comment on some technical topic your team is discussing you can point to him and say something like "Look at this genius - he hasn't got a clue what we are talking about but he still butts in with his usual nonsense". If on some day he remains quiet and does not butt into your discussion, comment on that to your team loudly so he can hear, "Look the genius did not butt in today with is usual nonsense" and laugh derisively. If you are discussing a problem with your team, remark loudly "Maybe we should give this problem to Einstein over there, he will of course solve it in a second", followed by sneering laughter. I think that gives you an idea of what I am trying to describe.
Always treat the narcissist the exact same way s/he treats you.
No one can reason with a narcissist. It will have no effect anyway because it is a mental disorder and narcissists are not reasonable people. If they ware reasonable people they would not be narcissists. It is only possible to deter narcissists, so that they will leave you and find another prey that is easier to victimize. It is a very bad idea to suddenly feel compassion for a narcissist and go easy on him/her in the middle of the deterring action. The narcissist will not understand your compassion but will see it as a victory for him and so his behavior will become even worse.