Badminton Safety is not too much a concern if you take reasonable care. Badminton is not a contact sport and therefore is a relatively safe game and the risk of getting injuries is not high.
Warming up before play is important and will reduce the chances of muscle and joint injuries. You can start with general warm up like stretching and jogging. Then spend some time on specific warm up like playing gentle shots for the first 2 -3 minutes with another player. Gradually upping the pace and tempo.
On average, players need about 15 minutes to warm up themselves. I would suggest that you do that too. Cooling down after play is important in preventing injuries. Avoid lying down straight after play. You can walk around or just do a few simple stretching exercises to cool down and relax your body.
Take extra care in cold halls where keeping warm between games is important. Put on a tracksuit or an extra layer of clothing to gradually cool down your body after a game.