Annex V point 5.4.2 of Directive 2005/36/EC lists the veterinary training certificates that are automatically recognised in EU member states. A veterinary degree must be listed here, or accompanied by a conformity certificate, for automatic recognition to apply.
Anhang der EU-Richtlinie 2005/36/EG
Anhang V Tiermedizin
Annex V 5.4.2
This means that veterinarians are subject to the same system as physicians (5.1.1), dentists (5.3.2), and pharmacists (5.6.2): anyone who graduates from a university listed there within the EU has their diploma automatically recognised in the other member states.
The prerequisite is a minimum training period of five years at a university or equivalent institution. Locations outside the EU are not covered by this provision.
Free and no obligation.