The corporation said on Friday that it had decided Lineker would take a break from presenting the highlights programme until an agreed and clear position on his use of social media had been reached.
Lineker, 62, has been embroiled in a row over impartiality after comparing the language used to launch a new Government asylum policy with 1930s Germany on Twitter.
The announcement by the BBC prompted pundit and former Arsenal striker Wright to tweet that he would not be appearing on Saturday in solidarity.
