With safely managed water accessible to only 19% of the population in Ghana, the majority of its residents are at risk of drinking contaminated water. Furthermore, this water could be a potential vehicle for the transmission of antimicrobial-resistant bacteria. This study assessed the presence of bacteria and the antibiotic resistance profile of Escherichia coli and Pseudomonas aeruginosa in drinking-water sources using membrane filtration and Kirby–Bauer disc diffusion methods. A total of 524 water samples were analyzed for total coliforms, total heterotrophic bacteria, E. coli and P. aeruginosa. Samples included sachets, bottled water, tap water, borehole and well water. Most of the sachet and bottled water samples were within the limits of Ghana’s standards for safe drinking water for the parameters tested. Over 50% of tap and borehole water was also free of E. coli and P. aeruginosa. Overall, of 115 E. coli isolates from tap and ground water samples, most were resistant to cefuroxime (88.7%), trimethoprim–sulfamethoxazole (62.6%) and amoxicillin–clavulanate (52.2%). P. aeruginosa isolates were most resistant to aztreonam (48%). Multidrug resistance was predominantly seen among E. coli isolates (58%). Evidence from this study calls for routine antimicrobial resistance surveillance in drinking water across the country and additional treatment of water sources at household levels.