Incineration is a common technique worldwide for treating Municipal Solid Waste (MSW). However, incineration residues (e.g., bottom and fly ash) require special treatment to prevent environmental risks due to the high content of heavy metals. The present study evaluated the stabilization degree of Pb, a toxic heavy metal in MSW incineration fly ash (IFA) treating by size-fractionated natural fishbone (FB) hydroxyapatite (HA). Bones from various fish species were used at different size fractions (<600 μm, 600 μm–2 mm, and 0–2 mm). The effect of different fishbone hydroxyapatite (FB-HA) sizes was studied by batch tests under the FB/IFA ratios of 0.0 and 1:10 (wt.), the contact or settling time of 6, 12, 24, and 672 hours, and the fixed W/S ratio of 1.5 mL/g. Using only 10% FB, Pb stabilization efficiency after 672 hours obtained 95.55% and 94.24% for FB sizes <600 μm and 600 μm–2 mm, respectively, and about 86.1% for non-fractionated FB (0–2 mm). The results indicated that contact time was the most critical factor for enhanced Pb stabilization. The FB particle size of 0–2 mm was deemed appropriate for Pb immobilization in short and long time settling periods. The adsorption isotherms were fitted well with the Langmuir and Freundlich models. The RL values of the Langmuir model were less than one and the n values of the Freundlich isotherm lie between 3 and 5, conferring the favorable adsorption of Pb to FB-HA for all size fractions.