Climate change has significantly altered species distributions in the wild and has the potential to affect the interactions between pests and diseases and their human, animal and plant hosts. While several studies have projected changes in disease distributions in the future, responses to historical climate change are poorly understood. Such analyses are required to dissect the relative contributions of climate change, host availability and dispersal to the emergence of pests and diseases. Here, we model the influence of climate change on the most damaging disease of a major tropical food plant, Black Sigatoka disease of banana. Black Sigatoka emerged from Asia in the late twentieth Century and has recently completed its invasion of Latin American and Caribbean banana-growing areas. We parametrize an infection model with published experimental data and drive the model with hourly microclimate data from a global climate reanalysis dataset. We define infection risk as the sum of the number of modelled hourly spore cohorts that infect a leaf over a time interval. The model shows that infection risk has increased by a median of 44.2% across banana-growing areas of Latin America and the Caribbean since the 1960s, due to increasing canopy wetness and improving temperature conditions for the pathogen. Thus, while increasing banana production and global trade have probably facilitated Black Sigatoka establishment and spread, climate change has made the region increasingly conducive for plant infection. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.