Kitchen sink drain pipe leaking inside the wall

As Ecnerwall stated break open the wall to locate exactly where the leak is coming from. A common plumbing orientation that you may notice inside your wall is for the trap pipe after entering the wall will connect to the center of a Tee fitting. The top connection is the drain vent (which goes to the roof) and the bottom leads the water to the main drain pipe.

Depending on what fitting/connection is leaking you will need to remove and replace it.

ABS pipe and fittings are welded together (just like PVC) with an ABS glue. If you are comfortable with cutting out the fitting and/or pipe the repair is fairly straight forward.

It sometimes helps to enlarge the wall opening as this allows more movement of the pipes and gives you more freedom to work.

There are fittings called "No-Hubs" which are basically rubber fittings that need no glue and are tightened by a hose clamp. These are much more forgiving and can be re-positioned anytime. They're sized for 1 1/2"-4" pipes and are commonly found as couplings, but also Tee's.