None of the tools in the stack currently support doings this, but it is quite easy to do that outside Elastic or Logstash, you just need to query elastic and then run your script.
I have a couple of python script that do exactly this, query a specific index for a specific event and if this is found it will trigger other actions.
You also have third party tools, like ElastAlert2 that makes it even easier: Alerts — ElastAlert 2 0.0.1 documentation