Depends, but mostly no. Many curries, especially Indian ones, feature a tomato base. They mostly contain spices, meats, and veggies, which means they're pretty damn good for you. Some include dairy, but not in any quantity that would make them unhealthy.

Japanese curries frequently have a roux base which is made from flour, butter, and spices, and may contain broth to thin the roux out. But aside from possible carbs from the flour roux, again it's all pretty innocuous.

The only contender for curry that may not qualify as healthy is kaeng or Thai curry. They almost exclusively use coconut milk as a base, which is pretty high in saturated fat. Aside from that, again it's mostly just meats and veggies, but the coconut milk is similar to butter or cream in terms of calorie density and dietary fat. (Saturated fat isn't necessarily bad for you by default, but it can raise cholesterol and cause other heart health issues if consumed in excess without burning it off with exercise. It's not like trans fat what is pretty much terribad for you no matter what lol)

Sorry if this is a lot of info. Curry is my favorite food, and my specialty as a chef