No, you don’t need that. You don’t have to be a vegetarian to practice yoga and to benefit from it. Yoga isn’t a club of people united by gastronomic predilections; yoga does not impose people of any kind of hard dietary restrictions or lifestyle. The ideal of yoga is freedom: if you decide to become a vegetarian, it should come naturally, without undue violence against yourself.
Vegetarians have two components regarding this issue: the physical aspect - how harmful or helpful to the body is not to eat meat and fish, and the moral aspect - eating of this food. The physical aspect is very individual and depends, inter alia, on the physical condition of the body.
The moral aspect is not that simple, because sometimes for the reception of full vegetarian food in modern civilization is necessary to make activities like to process fields with pesticides and as a result innocent living beings die and this food is not healthy at all.