It is the latest blow for the company, which last month announced job cuts and studio closures.
The change, which will take place from 31 March 2013, ends Zynga's ability to promote its Zynga.com platform on Facebook.
The move also means it will no longer be required to display Facebook advertising on its own site.
"There was plenty of speculation Zynga was getting referrals within the Facebook community that other gaming companies weren't getting which helped drive web traffic to Zynga games," Digital World Research chief executive PJ McNealy said.
Facebook said the move would bring its relationship with Zynga in line with other games studios.
"We have streamlined our terms with Zynga so that Zynga.com's use of Facebook Platform is governed by the same policies as the rest of the ecosystem," the social network giant said in a statement.
"We will continue to work with Zynga, just as we do with developers of all sizes."
Recent figures suggest 80% of Zynga's revenue comes from Facebook users.