The prevalence of disinfection by-products in drinking water supplies is a global concern due to their carcinogenicity. However, the monitoring of DBPs such as trihalomethanes (THMs) and haloacetic acids (HAAs) in drinking water supplies is non-existent in many developing Asian, South American, and African countries. The formation of THMs during disinfection arises from a reaction between the disinfectant and natural organic matter in the water, particularly, dissolved organic carbon (DOC). This reaction is hastened by increases in temperature, high levels of disinfectant doses or residual, elevated water pH, long disinfection contact times, and high DOC concentrations. However, the inclusion of a granular activated carbon adsorption process in the water treatment process is the most effective method for the removal of the main precursor (DOC) for the formation of THMs in treated water. The Barekese WTP, which disinfects with chlorine, has no adsorption process for DOC removal, and supplies over 80% of pipe-borne water to the city of Kumasi in Ghana, was assessed for the THM formation potential (THMFP). A THM predictive model was used to determine the potential THM concentration in the final water. The THMFP at the Barekese WTP ranged between 22.42 and 38.94 µg/L, which was below the 100 µg/L threshold set by the WHO. The lifetime average daily doses were 3.9494 × 10−4 µg/Kg/d and 3.9294 × 10−4 µg/Kg/d for male and female consumers, respectively. The lifetime integrative cancer risks associated with consumption of the water were 1.817 × 10−5 and 1.808 × 10−5 for males and females, respectively. The cancer risk posed was acceptably low. However, direct measurement of DBPs is required to corroborate these findings and verify the cancer risk posed to the consumers of treated water from the Barekese WTP to inform policies, regulations, public health interventions, and investment.