Sometimes, and you can't tell from the cheese itself. It comes down to the rennet, the enzyme used to turn milk into curds.
Traditional rennet comes from the stomach lining of young ruminant animals like calves, lambs and kids. Cheese made that way isn't vegetarian. But there are other kinds:
- Microbial rennet is made from molds or other microbes.
- Fermentation-produced chymosin is the same enzyme found in animal rennet, made by cultured microbes instead of taken from an animal. It's widely used, especially in the US.
- Vegetable rennet comes from plants such as thistle, and is used in some traditional cheeses.
Reading the label: look for "vegetarian rennet" or "microbial enzymes." A label that just says "enzymes" or "rennet" doesn't tell you, and if it says nothing at all, the cheese was most likely made the traditional way. Some protected-origin cheeses, Parmigiano Reggiano for one, are required to use animal rennet, so check those even if you assume they're safe. When in doubt, ask the producer or your cheesemonger.
Related: What is rennet? · What does DOP or PDO mean on a cheese? · What is the difference between raw milk and pasteurized milk cheese?