Plant and animal tissues adopt curved shapes through buckling and folding instabilities. Developing tissues constitute examples of active matter and in many cases the underlying forces are contractile in nature. Here, we study the dynamics of initially homogenous, self-organizing thin elastic actin sheets that contract due to the activity of myosin motors. Motor-induced contraction starts at the system boundaries which later proceeds into the gel bulk resulting in spontaneous buckling of the sheet. The appearance of wrinkles is intimately linked to the development of nonlinear gradients in the gel density that develops spontaneously during contraction. The final patterns resemble wrinkled plant leaves. The buckling instability reported here is complementary to the buckling and folding of expanding tissues and offers a well-controlled system to study mechanically induced spontaneous shape transitions in active matter.