Strengthening the governance capacity of local governments in the digital domain is crucial to the modernization of the national governance system and the process of sustainable development. This paper integrates the concept of sustainable development drawing upon the principles of systems theory and adopts the logical analytical framework of “resource input–process transformation–result output” to construct a digital governance capacity indicator system for local governments. The focus is on three dimensions: basic resource input, network public opinion management, and digital service effectiveness. Using statistical data from the digital governance capacity indicators of 14 cities and prefectures in Hunan Province from 2018 to 2022 as a case study, we base our analysis on the index system constructed herein. Employing the entropy-weighted TOPSIS method and the obstacle degree model, we evaluate and analyze the digital governance capacity of the government in Hunan Province. Our findings indicate that the government’s digital governance capacity in Hunan Province has been on a rising trend overall. However, there are noticeable regional disparities in the strength of digital governance capacity across western, northern, central, and southern Hunan, particularly in terms of digital service effectiveness, which presents the most significant barriers to improvement. These results suggest that local governments should tailor their efforts to enhance digital governance capacity around resource allocation based on regional differences, the establishment of an online public opinion monitoring system, the optimization of government information disclosure mechanisms, the performance of government service platforms, and the strengthening of a two-way communication mechanism between the government and the public.