An image pickup apparatus which is capable of reducing erroneous shooting when a third party other than a photographer has come within the field of view. A first detection unit detects a subject from first image data obtained as a result of shooting by a first image pickup unit. A second detection unit detects a subject from second image data obtained as a result of shooting by a second image pickup unit. When the first detection unit detects, from the first image data, the subject detected by the second detection unit, a shooting process is carried out in which a shooting operation is performed using the first image pickup unit, and image data obtained by the shooting operation is recorded.