Italy doesn't have one unified national pet-emergency number the way it does for human medical emergencies. The number 118 — Italy's ambulance and public emergency line — can sometimes help locate the nearest on-call vet, and in some regions it genuinely does coordinate this kind of support, but this isn't guaranteed nationwide.
The far more reliable approach outside the biggest cities is Italy's rotating on-call vet system: search 'veterinario reperibile' or 'guardia veterinaria' plus the town name to find the vet currently on duty for nights and weekends in that area. Most towns and smaller cities rely on this rotation rather than a single dedicated clinic — the on-call vet changes on a schedule, so the search needs to happen close to when it's needed, or you'll want to identify the local rotation system in advance. Larger cities additionally have dedicated round-the-clock hospitals, covered on the 24-Hour Clinics page.