Sure....you can chip out on side of the sold mortar, take some Quicrete in a tube available at lowes or Depot....butter the back of the brick...and sides....slide into place and wipe away any excess mortar. You use this product with a caulk gun so it is homeowner friendly. What color is the original mortar....this product comes in grey. If a different color....remove enough of the new mortar to skim back over with a matching mortar later on.

Is this a decorative brick veneer? or more of an old school brick column?

if the former than Handys advise above will work. If this is a "structural" job you might want to have a mason look at it. If one brick has become lose others may be in jeopardy.

I would agree with Handy on this. They make cement mortar in tubes. You can also if its really necessary to match the joints purchase a color powder that you can in this case rub onto the soft surface changing the color to match. However if you simply leave it alone, it will in a few short months then to blend right in with the rest.