Is it normal for cats to throw up once a week?

It’s common but it isn’t normal. Cornell flags vomiting more than once a week as outside the normal range and worth a vet conversation. Lots of cats vomit weekly, and lots of those cats are fine, but the frequency is information you shouldn’t ignore. The usual culprits are dietary (fast eating, abrupt food changes), hairball cycles, or mild GI inflammation. If your cat is otherwise well, try setup fixes for a week: slow-feeder bowl, a partial switch to wet food, daily brushing for long coats. Track whether the frequency drops.

When to call a vet: if weekly vomiting persists despite setup changes, or comes with blood, weight loss, lethargy or appetite loss, see your vet.