Encouraging meat eaters to eat more vegetarian foods benefits public health and environment. This study examined whether changes in menu design, specifically in the labeling of a dish, increases vegetarian food choice. In an online survey experiment involving a representative sample of Danish meat eaters (n = 955) we investigated the frequency with which dishes are chosen when they have a neutral vegetarian label (with no explicit indication that the dish does not contain meat), an explicit label (as vegetarian, meat-free, vegan, or plant-based), or a label referring to meat. We also examined the role of individual characteristics of the diner (food neophobia, meat-eating identity, meat intake and ethical concern). We found that neutral labeling outperformed explicit labeling among all meat eaters (neutral 17%, meat 10%, explicit labels 5%–7%) and in two sub-groups, namely, non-reducers (who are not actively reducing their meat intake: explicit 3.4%, neutral 10.2%) and meat-reducers (explicit 14.4%, neutral 30.1%). We found no significant differences between the four explicit labels. We show that non-reducers with low meat-eating identity can be nudged to choose a neutrally labeled vegetarian dish, and that, among ethically concerned meat-reducers, the vegetarian dish is chosen more often when the dish is neutrally rather than explicitly labeled. Finally, we show that meat-avoiders (additional convenience sample, n = 148) were as likely to choose a neutrally labeled vegetarian dish as an explicitly labeled one. Our results suggest that neutral labeling sidesteps reactance and moral licensing effects in both meat-reducers and non-reducers, and that food outlets with meat-eating customers should carefully consider their use of explicit labeling and use neutral labeling for vegetarian dishes where possible.