Go2Linux posted a tutorial about disabling ping response in Linux

Ping is really useful, when you want to diagnose a network, to be sure you are able to reach a given computer, the good thing about ping is that it lets you know that both ways uplink and downlink are working.
Ping works by sending a package from the originating computer to the receiving one, once it reach the receiving computer, that computer (better call it device), respond with a similar message.
That way you are sure the path is working and that there is an IP enabled device on the other side.

  How to stop / disable ping response in Linux