Not necessarily but it will be preferred. Since, one who eats meat can cultivate a pure heart just as one who is vegetarian might have an impure heart. Many people have misunderstood that Lord Buddha is a vegetarian. This is not true since Lord Buddha consumed any kinds of alms food offered by devotees be it meat or vegetable. One has to understand that not all places Lord Buddha and his Sangha travelled to, for preaching of Buddhism, has fertile lands. Thus, the ease of obtaining meat will be much easier than vegetable.
But, Lord Buddha did mentioned that eating PURE meat is possible. So, how do we define what is PURE meat? Meat ordered or received by mistake. Leftover or discarded meat. Meat from animals that have died naturally or by accident for at least 16 hours (The number of hours is to ensure the consciousness has left the body). Meat from alms rounds as practised in the Buddhist tradition.
The Mahaparinirvana Sutta states that "...All monks who live purely and all Bodhisattvas always refrain even from walking on grass; how can they agree to uproot it? How then can those who practise great Compassion feed on the flesh and blood of living beings?..." However, Lord Buddha never made it a compulsory rule that all his devotees have to be vegetarians, but he strongly encouraged us to be.
The Lankavatara Sutta states that all true practitioners of the Bodhisattva path eventually stop meat-eating. In his previous lives, the Buddha as a Bodhisattva would rather cut his own flesh to feed an eagle than let it eat a dove. Thus, all advanced practising laymen are thus necessarily vegetarians, since they cannot bear the pain of sentient beings.