There is evidence that promoting school physical activity (PSPA) benefits children and adolescents, but little is understood about how this promotion may relate to academic achievement and school climate across varying levels of socioeconomic status (SES). Hence, the study aimed to address this knowledge gap by examining two main objectives: (1) determining the association between PSPA and academic achievement and school climate according to schools’ SES and (2) exploring the potential mediating role of PSPA in the relationship between schools’ SES and academic achievement and school climate. This cross-sectional study at the school level focused on 4,990 schools (including public, subsidized, and private schools) that participated in the National Educational Study 2018 (Chile), which was applied to primary schoolchildren (4th grade, aged 8–10 years). Schools were divided into non-PSPA (n = 4,280) and PSPA (n = 710) during the year 2018. Changes in academic achievement from 2017 to 2018 and school climate were considered. PSPA was associated with improvements in maths (low-SES OR: 1.80, p < 0.001) and reading (middle-SES OR: 1.45, p = 0.029; low-SES OR: 1.47, p < 0.001). The indirect effect (IE) showed that PSPA partially mediated the relationship between SES and academic achievement in reading (IE = 1.017; SE = 0.12; 95%CI, −1.27, −0.77), maths (IE = –1.019; SE = 0.12; 95%CI, −1.25, −0.78), and school climate (IE = –0.46; SE = 0.52; 95%CI, −0.56, −0.35). In conclusion, PSPA was linked to positive changes in academic achievement, especially among low SES, and PSPA presented a potential mediating role in the relationship between SES of schools and academic achievement and school climate.