The concept of Multi-Energy System (MES) has been identified as a succinct approach in minimizing the economic implications, reducing environmental hazards, and increasing the efficiency of an integrated energy infrastructure holistically. Nevertheless, whilst a great number of resources have been invested in achieving low carbon energy communities and energy infrastructure, limited research has been conducted towards the realization of zero-carbon (ZC) MES. In line with this, this paper developed a novel mathematical model for the optimal configuration of ZC-MES integrated with financial constraints. To achieve this aim, a novel mean–max approach is proposed in this study for the selection of the representative hourly data from the pool of available datasets. Next, mixed-integer linear programming (MILP) is formulated to describe the whole system, with the inclusion of new replacement cost formulation and financial constraints. The proposed approach is then verified using a developed residential district area in Hong Kong that was modeled using TRNSYS software as a case study under different scenarios. The simulation results show that the optimal investment cost obtained by the conventional approach can be further reduced by 2.90% through rational equipment configuration without violating the applicable constraints, while a financing rate of 5% and 10% on the additional funds under breakable constraint are of economic benefits to the investors. Hereupon, this paper provides a useful reference resource for energy planners, decision-makers, and academic researchers, on the feasibility of zero-emission in the energy sector and other related fields.