Radon is a major source of naturally occurring radioactivity, and its measurement is considered extremely important in radiation protection, given its association with lung cancer. This pilot study aimed to estimate the annual effective dose received by students and staff based on monitoring data on the concentration of radon in the buildings of al-Farabi Kazakh National University (Almaty, Republic of Kazakhstan), based on the distance to the tectonic fault. The measurements were recorded daily from February 2021 to September 2022 using a RAMON-02 radiometer (SOLO LLP, Almaty, Kazakhstan). All measurements were taken from the basement to the top floor under normal conditions of use. The average accumulated concentrations of radon in the studied buildings ranged from 16.34 to 78.33 Bq/m3, which is below the maximum level of 100 Bq/m3 established by the World Health Organization (WHO) and the legislation of the Republic of Kazakhstan (200 Bq/m3). Relatively high values were recorded in the basement of the Faculty of Physics and Technology building (282.0 Bq/m3 in winter, 1742.0 Bq/m3 in spring, 547.7 Bq/m3 in summer, and 550.7 Bq/m3 in autumn), which is located closest to the tectonic fault and poorly ventilated. In almost all rooms (94%), radon levels were within the WHO-recommended reference level. The averaged results show the influence of the distance to the fault on the average indoor radon levels. The annual effective dose of radon for university students and staff ranged from 1.09 mSv/year to 1.53 mSv/year. The excess lifetime risk of developing cancer ranged from 0.44% to 0.61%.