Abstract We have analyzed populations of blue straggler stars (BSSs) in 24 Magellanic Cloud (MC) star clusters using multi-passband Hubble Space Telescope images. We compiled a homogeneous BSS database, containing both traditional and evolved BSSs. We uncovered a sublinear correlation between the number of BSSs in the cluster cores and the clusters’ core masses, characterized by a power-law index of 0.51 ± 0.07. For low stellar collision rates, the mass-normalized number of BSSs depends only weakly (or perhaps not at all) on the collision rate, implying that the binary-driven BSS formation channel dominates. Comparison with simulations suggests that stellar collisions contribute less than 20% to the total number of BSSs formed. Further tests, including the analysis of the BSS-specific frequencies and their population numbers at larger cluster radii, suggest that binary interactions may be their main formation channel, hinting at an anti-correlation between a cluster’s binary fraction and its core mass.