We investigated the association between climate variables and pulmonary tuberculosis (PTB) incidence in Brunei-Muara district, Brunei Darussalam. Weekly PTB case counts and climate variables from January 2001 to December 2018 were analysed using distributed lag non-linear model framework. After adjusting for long-term trend and seasonality, we observed positive but delayed relationship between PTB incidence and minimum temperature, with significant adjusted relative risk (adj.RR) at 25.1 °C (95th percentile) when compared to the median, from lag 30 onwards (adj.RR = 1.17 [95% Confidence Interval (95% CI): 1.01, 1.36]), suggesting effect of minimum temperature on PTB incidence after 30 weeks. Similar results were observed from a sub-analysis on smear-positive PTB case counts from lag 29 onwards (adj.RR = 1.21 [95% CI: 1.01, 1.45]), along with positive and delayed association with total rainfall at 160.7 mm (95th percentile) when compared to the median, from lag 42 onwards (adj.RR = 1.23 [95% CI: 1.01, 1.49]). Our findings reveal evidence of delayed effects of climate on PTB incidence in Brunei, but with varying degrees of magnitude, direction and timing. Though explainable by environmental and social factors, further studies on the relative contribution of recent (through primary human-to-human transmission) and remote (through reactivation of latent TB) TB infection in equatorial settings is warranted.