It depends upon WHICH form of Taijiquan and exactly WHAT the nature of your back injury is.
Of the five main forms of Taiji, Yang and Sun style are perhaps the "easiest" on the body - the least likely to aggravate an existing injury, PROVIDED the instructor fully understands the body mechanics involved. Definitely stay away from Chen style - the rapid, forceful movements are contraindicated for back injuries.
The selling point for Taiji (at least how it is sold in the US) is that it is gentle and slow. This can be true but even slow movement can be harmful if performed improperly.
Ask your prospective instructor about proper spinal alignment ("Taiji Pole") and how he/she teaches and practices it before you sign up for classes. Watch a class if possible: there should be NO bending from the waist - the students should be carrying themselves as if balancing books on their heads. The only exception to this is "coiling", the horizontal rotation or "twisting" of the waist and hips, during certain movements. This can be minimized as long as the instructor is aware of your condition.
I've taught Taijiquan for over 40 years, and many of my students had some form of back injury. All of them have benefited from proper movement practice, so with a little bit of caution and research I would say that Taiji is an ideal exercise for you.