I think the better questions to ask yourself first are exactly what kind of minor injuries are you getting, and how is your overall health (i.e. why might your body be more susceptible to sustaining these smaller injuries?). There are a lot of precautionary measures you can take to make sure you stay injury free, but if you are malnourished or over training, then they might be unavoidable until you remedy the real problems.
Continue to warm up and stretch before you run. This ensures that your muscles have plenty of blood and oxygen already circulating through them, which helps you pump your legs and arms faster and run stronger. And the same goes for after your runs, too. You want to be sure that you are properly stretching, foam rolling, and taking care of yourself to recover well after your run so that you can strengthen your muscles. If you do not stretch after your runs, your muscles are more likely to get "cold" and maintain lactic acid build up, which results in extreme soreness. If you continually run on sore muscles with a lot of stored lactic acid, your muscles become more susceptible to minor tears and overcompensation. Basically, that looks something like this: if you fail to stretch your quads well enough after your runs, over time lactic acid will build up and cause intense soreness. Your brain, to avoid feeling that soreness during your run, may tell your legs to put more emphasis on your shins upon landing during your foot strike than on your quads. This could result in minor tears and painful shin splints.
You also need to make sure you are taking care of yourself in regards to nutrition and hydration. That means you need to be drinking plenty of water throughout the day and getting in enough calories to sustain your running, focusing on making sure you are getting plenty of carbohydrates to fuel your runs, fats to fuel your brain, cognitive abilities, and protection of your internal organs, and definitely protein to aid in the recovery process. If you think you might be running too much, consider scaling back and see if that makes you feel stronger and results in less injuries incurred. Oftentimes, us runners push ourselves to (and past) our physical limits. Our brains tell us we can do it and we push ourselves through it, but our bodies might be screaming that they have had enough and NEED rest. Tune into what your body might be telling you, and if it is asking for more consecutive days off than you are giving it, listen to it. You might find that you really need to take a couple of weeks off, in fact, before you come back to running.