Climate change and variability influence temperature and rainfall, which impact vector abundance and the dynamics of vector-borne disease transmission. Climate change is projected to increase the frequency and intensity of extreme climate events. Mosquito-borne diseases, such as dengue fever, are primarily transmitted by Aedes aegypti mosquitoes. Freshwater availability and temperature affect dengue vector populations via a variety of biological processes and thus influence the ability of mosquitoes to effectively transmit disease. However, the effect of droughts, floods, heat waves, and cold waves is not well understood. Using vector, climate, and dengue disease data collected between 2013 and 2019 in Kenya, this retrospective cohort study aims to elucidate the impact of extreme rainfall and temperature on mosquito abundance and the risk of arboviral infections. To define extreme periods of rainfall and land surface temperature (LST), we calculated monthly anomalies as deviations from long-term means (1983–2019 for rainfall, 2000–2019 for LST) across four study locations in Kenya. We classified extreme climate events as the upper and lower 10% of these calculated LST or rainfall deviations. Monthly Ae. aegypti abundance was recorded in Kenya using four trapping methods. Blood samples were also collected from children with febrile illness presenting to four field sites and tested for dengue virus using an IgG enzyme-linked immunosorbent assay (ELISA) and polymerase chain reaction (PCR). We found that mosquito eggs and adults were significantly more abundant one month following an abnormally wet month. The relationship between mosquito abundance and dengue risk follows a non-linear association. Our findings suggest that early warnings and targeted interventions during periods of abnormal rainfall and temperature, especially flooding, can potentially contribute to reductions in risk of viral transmission.