Generative recommendation (GR) aligns with advances in generative AI by casting next-item prediction as token-level generation rather than score-based ranking. Most GR methods adopt a two-stage pipeline: (i) \textit{item tokenization}, which maps each item to a sequence of discrete, hierarchically organized tokens; and (ii) \textit{autoregressive generation}, which predicts the next item's tokens conditioned on the tokens of user's interaction history. Although hierarchical tokenization induces a prefix tree (trie) over items, standard autoregressive modeling with conventional Transformers often flattens item tokens into a linear stream and overlooks the underlying topology. To address this, we propose TrieRec, a trie-aware generative recommendation method that augments Transformers with structural inductive biases via two positional encodings. First, a \textit{trie-aware absolute positional encoding} aggregates a token's (node's) local structural context (\eg depth, ancestors, and descendants) into the token representation. Second, a \textit{topology-aware relative positional encoding} injects pairwise structural relations into self-attention to capture topology-induced semantic relatedness. TrieRec is also model-agnostic, efficient, and hyperparameter-free. In our experiments, we implement TrieRec within three representative GR backbones, achieving notably improvements of 8.83\% on average across four real-world datasets.