All illnesses MAY cause them to have a lower appetite, but does not mean all of them will. To increase appetite first check your environmental perimeters. Are temps correct? Lighting and length of lighting? Is something causing the tortoise stress? Is it by itself or with another one or a group? Is he active? Is he soaking? Are you seeing stools? Is seasonal issues slowing him down? Once you check all these things along with the health, take a close look at the diet you are offering.
For the diet, offer him tempting things. Bright colorful food items like red sweet pepper or even a small piece of colorful, sweet, very ripe juicy fruit (keep in mind what species of tortoise you are working with on this one). Try different types of greens, weeds, or blooms. Try even a piece or two of Mazuri, if it is not normally on the diet. Is he eating anything or just not as much as you think he should be? Try changing where you have the food dish. Some like it near hides, some away from the light, some could care less where the dish is as long as there is food. Try changing how you prepare it. For instance chop it finer or not as fine, mix the foods in together better, perhaps even coat the food with something yummy and well loved (baby foods and fruits work great for this). Try feeding small amounts several times a day, rather then one large one. This also helps to find a time he may prefer to eat at or does a better job of eating. Perhaps giving him a warm soak and then try feeding, that is often a big help.
What species is your tortoise? How old (how big) is your tortoise? How long have you had your tortoise and how long has it been kept in it's current set up? How long has it not been eating?
I would not automatically assume that your tortoise is sick just because it is not eating without first making sure that all environmental conditions are within range for the species.