To reduce the negative environmental impact of cement production and preserve natural resources, an experimental investigation was conducted to study the performance of concrete specimens at different curing ages and to determine the compressive strength of these specimens by replacing cement with molasses. Experimentation was carried out on the concrete specimens at a temperature range of 25 °C to 30 °C; six specimens were cast for each replacement ratio, except for 0.75% wt. of cement (86.55 g) and 1% wt. of cement (113.6 g), where five samples were considered for each ratio. The average 28-day compressive strength of the conventional concrete specimens came out to be 29 MPa, but increased to 40 MPa with the addition of 0.25% wt. of cement molasses (28.85 g). It was observed that as the percentage of molasses waste in the concrete mix was further increased by replacing the cement, the compressive strength of the concrete specimens increased gradually and then significantly decreased. The findings shed light on the prospect of using molasses waste instead of cement in the concrete mix. Also, it is worth mentioning that about 30% of the cost–benefit was obtained with reference to that of conventional admixtures available in the market for the production of concrete. However, it is notable that a long-term durability study needs to be conducted before making it viable. This work not only addresses a sustainable and innovative method of waste management (SDG12), but also contributes to low carbon emissions (SDG13). The novelty of this work lies in the fact that no such kind of study has been conducted in Pakistan so far, in addition to the very limited international literature available, and, in particular, no evidence on the compressive strength results at higher molasses dosages, i.e., 1% wt. of cement (113.6 g) and 2% wt. of cement (230.8 g).