In recent decades, meat consumption has increased globally due to increased incomes. A consequence of increased red meat consumption has been the rise in greenhouse gas emissions and nutrition-related diseases. Consumption of antibiotic-free (ABF) poultry meat is a viable healthy and sustainable substitute that will cause less damage to humans and the environment in the long run. This study was undertaken due to the increasing importance of healthy food consumption to preventing nutrition-related diseases. The health food industry is still in its preliminary stages; for market development of organic broiler meat and movement toward sustainable production of ABF meat, the first necessary step is conducting empirical research on ABF poultry meat consumption and identifying factors that influence household consumption patterns of ABF poultry meat. Therefore, the objectives of this study were the investigation of factors affecting poultry meat consumption by consumers and ABF poultry meat preference. Comparing the results could reveal what percentage of consumers are able to buy healthier higher-priced antibiotic-free poultry meat. Data were collected from 360 completed questionnaires completed by households from the city of Mashhad, Iran via simple random sampling in 2021. To investigate the first objective, an ordered logit model was used. The results showed that age, the head of household’s education, awareness of the nutritional benefits of poultry meat, advertising, and family income were statistically significant determinants of poultry meat consumption. To investigate the second objective, since some consumers cannot buy ABF poultry meat due to the higher prices, we used a two-step Heckman model. The results showed that the awareness of the nutritional benefits of ABF poultry meat, the head of household’s education, monthly family income, and advertising had positive impacts, with prices having a negative impact on the amount of antibiotic-free poultry meat consumed by the households. Comparing the results of the two models revealed that only about 30% of consumers could buy ABF poultry meat, mainly due to the higher prices. This study recommends improving consumer awareness, targeted distribution of ABF poultry meat according to customers’ economic and demographic characteristics, affordable prices, and appropriate marketing tools for sustainable consumption of ABF poultry meat.