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Abstract It is generally accepted that the Moon accreted from the disk formed by an impact between the proto-Earth and impactor, but its details are highly debated. Some models suggest that a Mars-sized impactor formed a silicate melt-rich (vapor-poor) disk around Earth, whereas other models suggest that a highly energetic impact produced a silicate vapor-rich disk. Such a vapor-rich disk, however, may not be suitable for the Moon formation, because moonlets, building blocks of the Moon, of 100 m–100 km in radius may experience strong gas drag and fall onto Earth on a short timescale, failing to grow further. This problem may be avoided if large moonlets (≫100 km) form very quickly by streaming instability, which is a process to concentrate particles enough to cause gravitational collapse and rapid formation of planetesimals or moonlets. Here, we investigate the effect of the streaming instability in the Moon-forming disk for the first time and find that this instability can quickly form ∼100 km-sized moonlets. However, these moonlets are not large enough to avoid strong drag, and they still fall onto Earth quickly. This suggests that the vapor-rich disks may not form the large Moon, and therefore the models that produce vapor-poor disks are supported. This result is applicable to general impact-induced moon-forming disks, supporting the previous suggestion that small planets (<1.6R_⊕) are good candidates to host large moons because their impact-induced disks would likely be vapor-poor. We find a limited role of streaming instability in satellite formation in an impact-induced disk, whereas it plays a key role during planet formation.