I work for a large company. I have 10 sick days per year. I fell ill and needed to use a sick day. My supervisor told me that I needed to make up the time on my next scheduled day off. This doesn't seem right. What should I do?

What does company policy dictate?

It's the time of year when employees decide to use or lose their sick days, and companies do whatever it takes to discourage that. So if you aren't really sick, and you want your next review to go well instead of being laid off or fired or just not given a raise, then don't call in sick, or make up the day's work.

Did you not use up all your days? As joy pointed out, this could be just the time of the year. You might want to discuss this with your HR dept.

You don't say if you will be paid for that makeup day or not. In many instances, overtime (premium pay) is not required to be paid until the employee has worked (not counting the sick day) 40 hours. So the supervisor may be trying to keep production up and do it most economically for the company.
Could this be your misunderstanding what the supervisor was telling you? In other words, was the boss talking about making up lost work and not about making up a full week's pay? If not, you don't have the sick days you think you have, you haven't followed the company policy for documenting sick leave or when it can be used, you didn't call in per policy, or the supervisor is trying to pull a fast one. And in most companies, in order for the supervisor to do that, he/she would have to record the day you were off as a day without pay. And all depends on where you are located and we don't know that.