I would definitely adjust the truing of the wheel. You don't want the wheel rubbing the brake; that will cause drag and wear on the brake and might cause problems (as in locking up the wheel) when braking. You also don't want to loosen the brake to prevent the rub, as that defeats the purpose of having brakes in the first place.
Note that I've had broken spokes often enough when commuting and touring that I carry a spoke tool in my kit for precisely this reason.
Based on my experience (which, in this at least, sadly is not minimal) I would add 1/4 turn of tension to the spokes ahead of and behind the broken spoke on the same side of the wheel, and take about the same amount of tension off the spokes ahead and behind on the opposite side of the wheel. You'll probably need to put on a bit more tension if it's on the drive side, take off less if it's on the non-drive side. (Note: this is based on a 36-spoke 3-cross wheel; if yours differs so will the required change.)
I tend to favour adding/removing tension by a fixed size movement instead of working to get the wheel completely true, since it's much easier to revert a constant amount of change when replacing the spoke. When you put the new spoke on, undo all your tension changes and you should be able to re-true the wheel using just the new spoke.
Obviously you're adding tension to some spokes, so the wheel won't be evenly tensioned; the idea here is to keep you moving long enough to get the spoke replaced. The adjacent spokes on the same side, and especially the trailing spoke, are substantially more likely to break. This is even more true on the drive side, where the power from the hub to the rim is primarily transmitted.
Your goal is to have a safe ride to the bike shop to buy a replacement spoke. :)
When you do replace the broken spoke, take the opportunity to inspect the adjacent spokes for damage and, if necessary, replace those too. It's vastly easier to do it once than have to do the same thing again the next day. And often there is an external cause for broken spokes, like chain damage, that can affect several spokes at once.
(There was one day on a trip when I walked the last 1/2km to a bike shop after the 3rd spoke in succession broke on the drive side of the rear wheel. Chain damage. Replaced those three and the next one too, was fine for the next 1000km.)