To reduce multiuser interference and maximize the spectrum efficiency in frequency division duplexing massive multiple-input multiple-output (MIMO) systems, the downlink channel state information (CSI) estimated at the user equipment (UE) is required at the base station (BS). This paper presents a novel method for massive MIMO CSI feedback via a one-sided deep learning framework. The CSI is compressed via linear projections at the UE, and is recovered at the BS using deep plug-and-play priors (PPP). Instead of using handcrafted regularizers for the wireless channel responses, the proposed approach, namely CSI-PPPNet, exploits a deep learning (DL) based denoisor in place of the proximal operator of the prior in an alternating optimization scheme. This way, a DL model trained once for denoising can be repurposed for CSI recovery tasks with arbitrary linear projections. In addition to the one-for-all property, in comparison to the two-sided autoencoder-based CSI feedback architecture, the one-sided framework relieves the burden of joint model training and model delivery, and could be applied at UEs with limited device memories and computation power. This opens new perspectives in the field of DL-based CSI feedback. Extensive experiments over the open indoor and urban macro scenarios show the effectiveness of the proposed method.