Facing the global climate change crisis, many cities have proposed the goal to achieve net-zero carbon cities. The natural carbon sink in urban space is indispensable for net-zero carbon cities, but the existing measurement system has shortcomings in the measurement elements and precision. This leads to unclear control objectives and elements of spatial planning, and the relevant planning strategies lack the support of quantitative results. We included the often-ignored natural carbon sink space and soil in the measurement scope. Taking Hangzhou as an example, we built a natural carbon sink capacity measurement system with respect to the carbon sequestration and storage capacity, measured the natural carbon sink, and evaluated its carbon neutrality’s contribution in urban space. The results showed that the carbon sink capacity of soil and small green spaces in built-up areas could affect the quantity and spatial pattern of the measurement results. Both should be included in the measurement system to improve corresponding spatial planning strategies’ reliability and feasibility. Additionally, Hangzhou’s annual natural carbon sequestration offset approximately 9.87% of the carbon emissions in the same year. With respect to the contribution to carbon neutrality, the role of natural carbon sinks in urban space was necessary, but the effect was limited. Therefore, strategies to reduce carbon emissions are integral for the net-zero carbon goal. Some spatial planning strategies to improve the urban natural carbon sink capacity are discussed. A more precise and comprehensive understanding of the urban natural carbon sink capacity can support the construction of a net-zero carbon city better.