I recently installed Kali Linux 2016.1 and did an update.
The whois command works fine.

 root@Kali:~# cat /etc/issue
 Kali GNU/Linux Rolling \n \l
 
 root@Kali:~# dpkg -l whois

 ||/ Name Version Architecture Description
 +++-=====================-===============-===============-================================================
 ii whois 5.2.12 amd64 intelligent WHOIS client

 root@Kali:~# whois www.google.com

 Whois Server Version 2.0

 Domain names in the .com and .net domains can now be registered
 with many different competing registrars. Go to http://www.internic.net
 for detailed information.

 Server Name: WWW.GOOGLE.COM.AR
 Registrar: ENOM, INC.
 Whois Server: whois.enom.com
 Referral URL: http://www.enom.com

You can try to install manually:

 root@Kali:~# apt install whois
 Reading package lists... Done
 Building dependency tree 
 Reading state information... Done
 whois is already the newest version (5.2.12).


 root@Kali:~# apt-cache policy whois
 whois:
 Installed: 5.2.12
 Candidate: 5.2.12
 Version table:
 *** 5.2.12 500
 500 http://http.kali.org/kali kali-rolling/main amd64 Packages
 100 /var/lib/dpkg/status