One word: Severely.
Of all the musicians in a group, the singer must be the most concerned about getting enough sleep. And the older you get, the more important this becomes.
You should also be concerned about staying hydrated, meaning: drink a lot of water. Be careful with alcohol or caffeine or smoking, all of which can fatigue the voice due to depriving the mouth and larynx of moisture, leading to fatigue and strain when you sing.
If you have had too little sleep and too little hydration, and you sing anyway, you will increase the likelihood of straining and injuring your voice by singing. So if there is a day that you have not had enough sleep, try to sing less and talk less also.
If you develop severe voice problems, the first thing a doctor will tell you is to stop singing and talking for a week, a month, or longer, and to stop rehearsing and performing until you have healed. You do not want to let things get that bad.
Some people are more prone to vocal problems than others. Simply be mindful of how you feel each day, and figure out what you should do to protect your voice from unnecessary strain. But of course you must also practice singing to keep your voice strong. You are like an athlete; you want to keep your physical training up, but you do not want to risk injury from too much exertion.
Your voice must last your entire life, so if you are serious about singing your best, be mindful of all the advice on this page.