It follows controversy over comments he made criticising the UK government's asylum policy this week.
“The BBC has been in extensive discussions with Gary and his team in recent days. We have said that we consider his recent social media activity to be a breach of our guidelines.
“The BBC has decided that he will step back from presenting Match of the Day until we’ve got an agreed and clear position on his use of social media. When it comes to leading our football and sports coverage, Gary is second to none...
"We have never said that Gary should be an opinion free zone, or that he can’t have a view on issues that matter to him, but we have said that he should keep well away from taking sides on party political issues or political controversies.”
Match Of The Day airs Saturdays on BBC One.