This is a big question, as a simple answer, it depends partly how you define exercise, and secondly on the class style.
If your definition of exercise involves raised heart rate, exertion and sweat then by and large yoga won’t meet that definition, and certainly my style of teaching won’t. However if you are open to a more subtle approach to exercise, slower more purposeful movement, exercise for mind and soul as well as body, then yoga fits that bill.
However different yoga teachers and class styles will vary. Some may be very physical, others much more mental/spiritual. Some of the physical classes may be more akin to a workout but these are probably a minority. Sometimes the difference between yoga and workout can be the intent created by the teacher; practice without focus is a workout; practice, however hard, with focus is yoga. As I mention above, though, this isn’t my style of teaching yoga.
By way of background, yogas history is one of evolution.
Some of the oldest systematic yoga writings are found in the Yoga Sutras, written around 3000 years ago. In here asana – yoga postures – occupies only a few lines, essentially reduced to cultivating a steady and still posture, and represents merely one of the eight so called limbs of yoga.
Written five hundred years ago the Hatha Yoga Pradapika deals with postural yoga much more extensively, from the position of starting with physical yoga postures as a gateway to the more subtle mind and spiritual aspects of yoga. However the physical postures here are slow and static – and absent is the flowing style of modern ashtanga of vinyasa practice, and the popular sun salutation sequence you find in many modern classes.
Modern Hatha yoga shows further evolution, with faster flowing styles, slower more methodical styles and countless variations. Arguably this is an adaptation to the modern world. although the counter argument is that in some cases the higher aims of yoga are left behind.
So in some ways there is no definitive answer to the “Is yoga exercise?” question. Largely the answer is one of intent. In the opening verses of the yoga sutras we read “Yoga is stilling the thought waves of the mind” – this is exercise for the whole being and practice which honours this, and physical yoga postures or flow is but part of this.