We demonstrate spontaneous wrinkling as a transient dynamical pattern in thin freely floating smectic liquid-crystalline films. The peculiarity of such films is that, while behaving liquid-like with respect to flow in the film plane, they cannot quickly expand their thickness because that requires stacking of additional smectic layers. At short time scales, they therefore behave like quasi-incompressible membranes, very different from soap films. Smectic films can develop a transient undulation instability or form bulges in response to lateral compression. Optical experiments with freely floating bubbles on parabolic flights and in ground lab experiments are reported. The characteristic wavelengths of the wrinkles are in the submillimeter range. We demonstrate the dynamic nature of the pattern formation mechanism and develop a basic model that explains the physical mechanism for the wavelength selection and wrinkle orientation.