Due to the high propagation path loss in the millimeter wave (mm-wave) system, it is necessary to use the large antenna array for obtaining the high beamforming gain in mm-wave systems. In order to reduce the cost and complexity of hardware, an architecture called hybrid precoding is proposed, which divides the precoding operation into the analog domain and the digital domain. However, this poses a challenge for channel estimation in mm-wave systems. In addition, due to the great amount of users and antennas, the feedback overhead of channel estimation is also an issue that needs to be considered. In the letter, we consider the mm-wave massive multiple-input-multiple-output (MIMO) system and propose a federated learning (FL)-base channel state information (CSI) estimation and feedback (FCEF) scheme, where each user trains the local model through the local dataset and exchanges the model parameters with the base station (BS). Thanks to upload model parameters rather than huge channel data, the FCEF scheme has lower transmission overhead than centralized learning (CL). The architecture of the proposed FCEF model is described in the letter, which consists of a CSI estimation and compression (CEC) network and a CSI recovery (CR) network. Numerical results demonstrate that the proposed FCEF scheme has good performance for CSI estimation and feedback in mm-wave MIMO systems, which is close to that of the CL-based scheme while ensuring lower transmission overhead.