The answer to this is it depends on the level of pain you are experiencing. You also need to rule out that it is really a muscle pull and not something serious like a bone fracture, muscle tears or tendon injury.
Normally muscle pull occurs on the lower part of our body- anywhere from the hip to all the way down to our feet. Common reason for getting muscle pull is through a certain jerk movement when the muscles are not warmed up or rigorous exercise without proper warming up.
Once, I experienced a muscle pull. Actually I have not been working out at night time for a few weeks. I have transferred my workouts too morning time as I have made the changes- avoid bathing after the sun sets or after gym. But due to inability to wake up at times, guilt set in and I finally decide to go at night.
When I did my usual set of cardio, core strengthening exercises, strength training on the lower part of my body. After the strength training, I did some running on the treadmill for about 10 minutes.
The next morning, I started feeling a mild muscle pull on my left leg. By night time, the pain got worst. For the next one week, the pain woke me up from sleep at 2am or 3am- the pain shot from my right butt all the way to my knees and feet. It is unusual for me to have muscle pull because I’ve always warm up and cool down well- that’s why my sessions normally last between 1.5 to 2 hrs (I also love exercising).
Anyway, the experience have taught me that it is possible to continue to work out when there is a muscle pull on the lower torso but:
1. Take a rest the initial 2 to 3 days to see if the muscle pull will heal by itself.
2. If the pain is very much reduced, can begin exercising but reduce intensity.
Stick to cardio at the level you are comfortable with and preferably pain free. You can do exercises on the stationery bike at low effort levels so that it does not cause you pain.
3. Core exercises using the stability ball and medicine ball- it still works on your abdominal muscles but will not put any strain on your legs (as you are seated on the stability or exercise ball)
4. Stretch gently and to the extend where there is little pain.
It took about 10 days before I recovered. During that time, I still continue my workouts but at a lower intensity.
Even slow and steady, you will still burn calories. You’ve just got to be patient and extend your workout time.