Packaging is a leading factor determining the total environmental effect of food products. This study investigated consumers’ awareness, behavior and expectations in relation to the environmental sustainability aspects of food packaging. Using an online survey, responses from 646 participants were collected. The effect of socio-demographic characteristics on all variable responses was explored by ANOVA models and t-tests. Participants were segmented according to a visual approach based on a principal component analysis applied on the consumers’ behavioral data. Gender, age, and education level affected consumer awareness, behavior and expectations differently. Four groups of consumers were distinguished on the grounds of their behavior in relation to food packaging: (1) More sustainable—packaging-role-oriented; (2) More sustainable—packaging minimizers; (3) Less sustainable; and (4) Medium sustainable. The most sustainable groups were mainly composed of females, while less sustainable consumers were mainly the youngest. The four groups differed in terms of expectations for sustainability-related information that can be communicated through food labels. In conclusion, this work provided new knowledge that is useful to understand the factors that influence consumer behavior and to promote the consumers’ packaging-related sustainability choices through food packaging.