Solution: Allow ICMP requests from your corresponding Security group!
Here is how to do it,
1. Login to your AWS Console and from EC2 instance list, select the EC2 instance
2. Bottom, click on the Security Group Link
3. After SG page load, click on the Edit button
4. Leave all other rules as it is (as you would require this)
5. Click on Add Rule and under the type, Select ALL ICMP IPV4
6. Under Source Select Anywhere (or from your IP), (Please refer to the below image)
7. Save the settings
EC2 instance should be accepting ping requests now.