Firefighters were called to Leeds Rugby Academy off Bridge Road shortly before 3.30pm.
Leeds Fire Station watch manager Phil Rhodes said that a portable toilet behind the main building was thought to have been deliberately set alight.
Two bags of rubber balls used to construct some of the site's playing surface were also burned.
It is thought young people who were riding in the area on bikes could have started the fire.
Mr Rhodes said that staff from the the Kirkstall Road station took around half an hour to extinguish the blaze.
Black smoke cloud could be seen over the Kirkstall area during the afternoon.
The ground is used by the Leeds Rhinos and Yorkshire Carnegie.