Shearer is the second major pundit on the show to reveal such a decision in a sign of solidarity following Ian Wright's support for Lineker.
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Lineker has been taken off presenting duties for the BBC's hit football programme following an impartiality row.
He had criticised the UK Government's new asylum policy and compared the language they used for the bill to 'that used by Germany in the 30s.'
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Wright was quick to show his support for Lineker as he said on Twitter: "Everybody knows what Match of the Day means to me, but I've told the BBC I won't be doing it tomorrow. Solidarity."
His co-pundit eventually followed suit as he took to the social media platform to say: "I have informed the BBC that I won't be appearing on MOTD tomorrow night."
Lineker, Wright and Shearer form an iconic trio on the show that presents the highlights of the Premier League each weekend.
However, none of them will feature on this weekend's edition of the programme.
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It remains to be seen who will replace Lineker as the presenter, but Alex Scott appears to have ruled herself out of the running.
She tweeted: "FYI…" before adding a GIF saying: "Nah! Not me."
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Other likely candidates for the role could be Mark Chapman and Gabby Logan, both of whom have been long-standing presenters for the BBC.
There are also questions marks as to what pundits could appear, with former Manchester City right-back Micah Richards stating he will not be in the studio.
Richards tweeted: "I was not due to be working on MOTD tomorrow, but if I was, I would find myself taking the same decision that Ian Wright and Alan Shearer have."
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A spokesperson for the BBC regarding Lineker said: "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.
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"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."
talkSPORT's Darren Bent believes Lineker has been the victim of 'cancel culture' as he slammed the BBC's decision.