A few practical notes from the data: every practice has its own website for checking hours before you call.
For urgent care, Kleintierpraxis im Dichterviertel lists emergency or out-of-hours services. Save the number before you need it; German out-of-hours care carries a legal minimum surcharge, so knowing where to go is half the battle.
New to Erfurt with a pet? Register the microchip with TASSO first (free, five minutes), then book a get-to-know visit with one of the practices above before you actually need one: being an existing patient makes urgent appointments far easier to get. Every listing shows the English-language evidence behind it, and the Confirm English button lets you strengthen it for the next owner after your visit.