SUMMARY Plant species with large genomes tend to be excluded from climatically more extreme environments with a shorter growing season. Species that occupy such environments are assumed to be under natural selection for more rapid growth and smaller genome size (GS). However, evidence for this is available only for temperate organisms. Here, we study the evolution of GS in two subfamilies of the tropical family Zingiberaceae to find out whether species with larger genomes are confined to environments where the vegetative season is longer. We tested our hypothesis on 337 ginger species from regions with contrasting climates by correlating their GS with an array of plant traits and environmental variables. We revealed 16‐fold variation in GS which was tightly related to shoot seasonality. Negative correlations of GS with latitude, temperature and precipitation emerged in the subfamily Zingiberoidae, demonstrating that species with larger GS are excluded from areas with a shorter growing season. In the subfamily Alpinioideae, GS turned out to be correlated with the type of stem and light requirements and its members cope with seasonality mainly by adaptation to shady and moist habitats. The Ornstein–Uhlenbeck models suggested that evolution in regions with humid climates favoured larger GS than in drier regions. Our results indicate that climate seasonality exerts an upper constraint on GS not only in temperate regions but also in the tropics, unless species with large genomes find alternative ways to escape from that constraint. Significance Statement The question of how species can adapt to periods of drought and drought stress is of great relevance in the current period of climate change and it is also worth asking whether mechanisms of adaptation are similar in different parts of the world. Here, we focused on the poorly understood but complex biomes like monsoon forest, tropical dry forest and tropical rainforest, while using the economically important family Zingiberaceae as a model group.