The shower cartridge that is hidden behind the shower handle needs to be replaced as it contains all the functioning seals in it the shut the water on and off.

98% of the time this will fix the issue. If it doesn't the valve body that the seals rest against may be pitted or cracked not allowing the proper seal to be made even if the seals are in perfect condition. If this is the case a new shower valve needs to be installed.

In this case I would have to recommend calling a plumber unless your experienced with proper soldering and pipe fitting procedures.

Good luck. Cartridge is what you need to replace first.