Exercise is certainly a mitzvah when done for health reasons. The Torah says "...Guard your life very carefully..." A person must do his all to preserve his health and prolong his life.
Maimonides states, "It is a positive mitzvah to remove any impediment that might pose a danger to life, and to be extremely cautious regarding this." Maimonides was a renowned physician and recommended exercise for preventing illness and for promoting good health.
But... there is no blessing one makes when doing the exercise mitzvah. Why not?
Since I'm Jewish, I'll answer your question with another question. What about other mitzvahs like honoring parents, visiting the sick and giving charity - all case when we also don't make a blessing? What's the rule for when "Yes" and when "No"?
There are many explanations given but I will give one here.
There are basically two categories of mitzvahs:
- Mitzvahs performed only at certain times, such as succah, matza and shofar. Since they are only done at specified times they bring a person to a special sense of joy and are preceded by making a blessing.
- Mitzvahs that obligate a person at all times, such as honoring parents, visiting the sick and giving charity. They are always "in play" and doing them therefore naturally lacks the same sense of joy. Less joy equals no blessing said for the mitzvah.
Exercise and promoting good health would be included in this second category. It is an ongoing mitzvah from which a person is never absolved.
One might say that exercising is doing a mitzvah whose real blessing is in promoting good health that will help a person accomplish as much as possible in life.
Which reminds me of a joke. A guy complained to his friend, "My doctor put me on such an exercise schedule! Every day, 50 push-ups, 100 sit-ups, and then a 20 mile run! It's so exhausting I can hardly stand it!"
"Wow!" said his friend, "When did you start?"
"I start tomorrow."