How can I easily inject a tone from a DAC into an XLR audio signal?
You want to first put the mic signal through a mic preamp, and then mix the preamp out with the DAC output. (The DAC output is presumably unbalanced and somewhere near line level, though it may want a bit of tweaking.) Any simple audio mixer with at least one mic pre will do this for you.

EDIT:
as the OP says that working at line level is not possible - it sounds like what is wanted is some sort of resistive mixing at mic level. This is likely to be fairly noisy though. There is also the issue of balanced versus unbalanced - the mic is (and really needs to remain) balanced (question: what kind of mic?) whereas the DAC output is unbalanced and much higher level. So not really possible to answer this properly without more details. And the question remains - why do you want to work at mic level?