An image pickup apparatus which is capable of enhancing the accuracy of shake correction. A shake-detecting sensor detects a shake of an apparatus body. A microcomputer computes a shake amount based on an output from the shake-detecting sensor. A camera signal processing circuit corrects motion of an image due to camera shake based on an output from the microcomputer. A rest-determining device determines, based on the output from the shake-detecting sensor, whether or not the apparatus body is at rest. A recorder records a picked-up image. A recorder vibration-determining device determines whether or not the apparatus body is vibrating due to vibration of the recorder. A cutoff frequency-setting device changes characteristics of the microcomputer based on a result of determination by the rest-determining device and a result of determination by the recorder vibration-determining device.