In most cases with public-facing instances, it is desirable by system administrators to allow ping reply as a basic means of verifying network response. This is a common AWS EC2 FAQ.

Create a security group (or use an existing one) and add a permission for ICMP IPs with a type and code of -1 e.g:

faq-AddIPs.png

Note: You can assign the IPs as 0.0.0.0/0 to allow all IPs and networks or restrict access with the appropriate CIDR notation.

Once added, the permission will be listed in the security group as follows: 

faq-Allow.png