Mechanical buckling is a ubiquitous phenomenon of elastic bodies like core-shell microgels. Although conventional theory predicts that sufficiently high pressure is the primary factor inducing the buckling of core-shell microgels, they often buckle spontaneously without applying pressure. We explored such spontaneous buckling of microgels by introducing interfacial tension between the gel phase of the shell and sol phase of the core. Thus, we found that the core-shell microgels in a sol-gel coexisting phase with a certain shell thickness ratio exhibit spontaneous buckling. According to our theoretical analysis, spontaneous buckling occurs due to the balance between the gel elasticity E and interfacial tension gamma when the characteristic length gamma/E is comparable to the microgel size R. Moreover, we found that the ratio between gamma/E and R determines the buckling condition of the shell thickness ratio. Our findings establish an important framework for applying spontaneous buckling to the shape control of elastic bodies.