The State of Veracruz (Mexico) is highly vulnerable to climate change. Therefore, it is necessary to identify and analyze local climate extreme trends and explore potential relationships between climate indices and maize. The objectives of this research were (1) to describe recent trends of climate indices (1979–2018) and (2) to compare these climate indices with maize yields produced in Veracruz, Mexico, under rainfed conditions. The methodology calculated and analyzed the sector-specific climate indices (Rx5day, PRCPTOT, SPI6, R20mm, TXx, TNn, TXgt50p, and TXge35) in 18 observation sites using Climpact. Climate indices were calculated over the spring-summer agricultural cycle and correlated with rainfed maize yields. Results show increasing trends for Rx5day, TXx, TXgt50p, and TXge35 indices in 65%, 56%, 89%, and 67% of the analyzed sites, respectively, whereas decreasing trends in PRCPTOT and R20mm indices were detected in 59% and 47% of the sites. Significant correlations (p < 0.05) between climate indices and maize yield were found in eight municipalities, of which 62% were positive. In conclusion, extreme temperature and precipitation local events are increasing in frequency, duration, and intensity, and depending on the site’s local climate, these might positively or negatively impact maize yields.