Green Hydrogen could be used as a sustainable cooking fuel, especially in countries of the global south in which cooking with carbon-based, or biomass fuels is prevalent. This paper presents a criteria based assessment of the sustainability of cooking with hydrogen in comparison to charcoal and liquefied petroleum gas. The research methodology adopts a systematic literature review to provide a comprehensive overview of the research. Based on this, a morphological analysis is conducted to display possible hydrogen cooking scenarios. A chosen hydrogen scenario is then subjected to a sustainability assessment and compared with the aforementioned conventional cooking methods. The findings of this paper reveal that while hydrogen presents itself as a potential alternative, it is currently not a more sustainable option. Despite its lower climate change impact when compared to liquefied petroleum gas and charcoal, hydrogen falls short in several other sustainability aspects, such as investment costs, marine and freshwater eutrophication or safety concerns related to the usage of the energy source.