Are there areas zoned against rentals?

[Hunter Eidmann]

I am curious if there are areas zoned such that they only allow people to buy homes there and not rent. I ask because I was on rent.com and when I searched an area near me, there were some places with tons of rentals and other places with square miles of land that has plenty of homes there but none for rent. If so, can someone please point me in the direction of a website that will show you areas zoned against renters? Thank you!