Increasing amounts of waste are incinerated every year; therefore, the amount of Municipal Solid Waste Incineration Bottom Ash (MSWI BA) also increases. At the same time, limited landfill space and the goal of achieving a circular economy dictate the search for MSWI BA applications. Large fractions are successfully used to replace aggregates in concrete, but the MSWI BA fraction < 3 mm has several disadvantages, such as high porosity and high contamination that make its application as aggregate or cement replacement difficult. However, finding a tailored treatment can turn these fines into a potential filler material (Minor Additional Constituent, MAC, 5% w/w) in Portland cement. This paper investigates milled fines that were produced out of MSWI BA fines (0.125–3 mm) to match the size distribution of CEM I 52.5 R and CEM I 42.5 N. They are also compared to the untreated fines (< 0.125 mm) from the same MSWI BA. The influence of milling on the fines was investigated by SEM (morphological analysis) and the leaching test to assess the potential environmental impact. Studied by isothermal calorimetry, the effect of the designed fines on cement hydration appears to be very small and the results for the mechanical performance of mortars show that all fines examined in the study might be considered as potential MACs.