As per the Salesforce documentation, Post-Install script can perform callouts using an async operation only.
So, I tried to do callout with future method. But, i'm not getting the session id in the future callout because of which i'm getting error while doing callout.
Note that the documentation states that a post install script:
can’t access Session IDs
so the session Id can't be included in a call to a future method.
I also tried with annotating the class as without sharing, but it didn't work. (InstallHandler runs under a special ghost user. What rights does it have?)
Is there any other way to do callout from Post-install script?