Can I injure myself doing yoga?

Yes, of course, as in many physical activities, e.g. running, playing rugby, etc.  The New York Times regularly publishes articles discussing yoga injuries.  In 2010, there were roughly 2500 yoga-related injuries appearing in emergency rooms of hospitals in the US.  From 2002-2010, 95% of all such yoga-related ER visits were minor, leading to patients being treated and released.  (One of these, on June 26, 2007, occurred when a 45-year-old woman was “riding bike to yoga class when yoga mat caught in wheel of bike causing fall head first to cement.”).

Compare this to the leading causes of ER visits, (#1, stomach pain, 10,000,000 visits in 2010).   Had yoga injuries been tallied separately, they wouldn’t have ranked in the top 100.

Nonetheless, be careful out there!  Listen to your bodies, and find good teachers who won’t be forcing your body into positions it’s not ready to adopt.