Can my work fire me because I was injured outside of work and am unable to work for 10 days?

Not being at work for your job can lead to legal termination

I'm going to change the topic to employment law so those who do it will see your question but as a general rule, you can be fired for any reason so long as it's not a bad reason, like race/religion...and being unable to do the job can be the basis of termination. Sorry

Your question displays a gap in the ADA and FMLA an injury which will heal in time does not earn you much protection,

If you were unable to perform your work duties and were away from your job for 10 days, your employer can terminate you unless you are protected by a union contract or your termination was based upon discrimination due to your membership in a federally protected class of persons (gender, race, age, etc.) Here is appears you just could not do you job. Your employer is not obligated to hold your job until you are able to return to work.

The answer to your question depends on a number of facts not addressed in your question, such as how many employees your company has, how long have you worked there, the nature of your duties, whether you had vacation time, etc. I suggest you contact an employment lawyer to discuss your case. Many of us will provide a free consultation.