What should I do with this crack on an outside brick wall?
Very unusual to have the crack extend through the brick. Usually, the mortar is designed to have less strength than the brick so when the wall settles it cracks staggering down the wall in the mortar joints only. That way, the mortar can be repaired without replacing bricks. (Finding bricks that match exactly will be difficult.)

Several possible issues: 1) settlement, 2) expansion, 3) bowing of wall. 

1) Vertical cracks are usually caused by differential settlement.  That is to say, as the load is transferred to the ground, the ground has soft spots that cause the wall to settle a different amount at different points along the wall. 

When this happens the crack will taper. That is to say, the crack opening will get bigger along the crack. Also, one side of the crack will drop from the other side. Neither of these issues happened, so I doubt settlement is your problem. 

If it is settlement, it would be so insignificant that it would not be “failure” (collapse). 

2) As a wall heats up and cools down it expands and contracts. If the wall is on the south side of the house (the side with the greatest heat gain and expansion) or if the wall is exceptionally long, expansion can occur. Cracking will occur at a weak spot, like below a window, etc. where there is less support (strength). 

If this occurs in solid wythe walls, it can crack through to the interior. Is it solid wythe brick wall and did it crack through to the interior? Does the crack extend through the foundation?

If the wall is a brick veneer wall, the backing support wall portion may or may not crack too. Is it a brick veneer wall? 

3) If the wall is bowing inward or outward it could cause the wall to crack. Is the wall straight? 

Regardless the type of wall, if water gets in the crack and then freezes, it will worsen (enlarge) the crack.