The row overshadowed a migration deal struck between British Prime Minister Rishi Sunak and French President Emmanuel Macron, with the BBC accused of bowing to political pressure.
"Gary Lineker off air is an assault on free speech in the face of political pressure," the opposition Labour party said, calling for the BBC to re-think its decision.
The Department for Culture, Media and Sport said: "Individual cases are a matter for the BBC."
MOTD commentator Steve Wilson later tweeted that the show's commentators had also pulled out from Saturday's broadcast, leaving BBC management reliant on World Feed commentary.
But the BBC said it considered his recent social media activity to be a breach of its guidelines.