Adequate utilization of services is critical to maximize the impact of counselling on infant and young child feeding (IYCF), but little is known about factors affecting utilization. Our study examined supply- and demand-side factors associated with the utilization of IYCF counselling services in Viet Nam. We used survey data from mothers with children <2y (n = 1,008) and health staff (n = 60) from the evaluation of a program that embedded IYCF counseling into the existing government health system. The frequency of never users, one-time users, repeat users, and achievers of the recommended minimum number of visits at health facilities were 45.1%, 13.0%, 28.4% and 13.5%, respectively. Poisson regression showed that demand-generation strategies, especially invitation cards, were the key factors determining one-time use (Prevalence ratio, PR 3.0, 95% CI: 2.2–4.2), repeated use (PR 3.2, 95% CI: 2.4–4.2), and achievement of minimum visits (PR 5.5, 95% CI: 3.6–8.4). Higher maternal education was associated with higher utilization both for one-time and repeated use. Being a farmer, belonging to an ethnic minority, and having a wasted child were associated with greater likelihood of achieving the minimum recommended number of visits, whereas child stunting or illness were not. Distance to health center was a barrier to repeated visits. Among supply-side factors, good counselling skills (PR: 1.3–1.8) was the most important factor associated with any service use, whereas longer employment duration and greater work pressure of health center staff were associated with lower utilization. Population attributable risk estimations showed that an additional 25% of the population would have achieved the minimum number of visits if exposed to three demand-generation strategies, and further increased to 49% if the health staff had good counseling skills and low work pressure. Our study provides evidence that demand-generation strategies are essential to increase utilization of facility-based IYCF counselling services in Viet Nam, and may be relevant for increasing and sustaining use of nutrition services in similar contexts.