Named Entity Recognition (NER) is an important task in information extraction. However, due to the lack of labelled corpora, biomedical NER has scarcely been studied in Vietnamese compared to English. To address this situation, we have constructed VietBioNER, a labelled NER corpus of Vietnamese academic biomedical text. The corpus focuses specifically on supporting tuberculosis surveillance, and was constructed by collecting scientific papers and grey literature related to tuberculosis symptoms and diagnostics. We manually annotated a small set of the collected documents with five categories of named entities: Organisation, Location, Date and Time, Symptom and Disease, and Diagnostic Procedure. Inter-annotator agreement ranges from 70.59% and 95.89% F-score according to entity category. In this paper, we make available two splits of the corpus, corresponding to traditional supervised learning and few-shot learning settings. We also provide baseline results for both of these settings, in addition to a dictionary-based approach, as a means to stimulate further research into Vietnamese biomedical NER. Although supervised methods produce results that are far superior to the other two approaches, the fact that even one-shot learning can outperform the dictionary-based method provides evidence that further research into few-shot learning on this text type would be worthwhile.