Current image encryption schemes do not achieve robustness to lossy compression and downsizing without sacrificing image quality. In this paper, we introduce a selective robust image encryption scheme for online social networks that provides a trade-off between robustness and security. With the selective encryption property, users have an option to share a blurred version of the original image and only a specific group of people having the right key can access the full content. Our method is based on the fact that image resizing and compression can be modeled as a low pass process which alters and/or removes high frequency components of image pixels. We achieve robustness to compression and downsizing by adjusting and shuffling DCT coefficients. Experimental results show that the proposed method can be applied in real world applications and social networks with satisfactory image quality.