The Match of the Day presenter was taken off air after tweeting about the UK government's new migration law, prompting a row over BBC impartiality.
Many UK-wide sports programme have already been hit by an impromptu staff boycott in support of Lineker.
BBC Scotland said it would only be able to bring "limited sport programming this weekend".
In a statement the corporation said: "Sportscene will run this evening on BBC One Scotland and BBC Scotland, with an amended format similar to current plans for Match of the Day.
"Some of the Sportsound slot on Radio Scotland was replaced by pre-recorded material.
"We are sorry for these changes which we recognise will be disappointing for BBC sport fans.
"We are working hard to resolve the situation and hope to do so soon."
The statement added schedules would be amended to reflect the changes.
It is unclear how planned BBC Scotland coverage of major sporting events on Sunday, including the Six Nations and Scottish Cup, will be affected.
The row began on Tuesday, when controversial plans were unveiled to ban people arriving in the UK illegally from ever claiming asylum.
The UK government says the tough measures are necessary to address a rise in the number of people crossing the Channel in small boats.
But Lineker reacted to it on Twitter calling it an "immeasurably cruel policy directed at the most vulnerable people in language that is not dissimilar to that used by Germany in the 30s".
The ex-England striker, who is employed by the BBC on a freelance basis, has hosted Match of the Day since 1999 and is the corporation's highest paid star, having earned about £1.35m in 2020-21.
BBC employees are expected to be remain impartial on political matters and must follow strict social media guidelines, but there is significant debate about how they should apply to staff outside of news.
After Lineker was suspended on Friday several high profile stars, including Ian Wright and Alan Shearer, confirmed they would not be appearing on Match of the Day.
BBC director general Tim Davie, who has said impartiality should be at the heart of the corporation, told a BBC journalist: "I think we always look to take proportionate action and that's what we've done."
By Saturday several BBC TV and radio sports shows had been pulled at the last minute, including Football Focus, Final Score and Fighting Talk.
First Minister Nicola Sturgeon is among those who have criticised the decision to suspend the former footballer.
On Friday she tweeted: "As a strong supporter of public service broadcasting, I want to be able to defend the BBC. But the decision to take @GaryLineker off air is indefensible. It is undermining free speech in the face of political pressure - & it does always seem to be rightwing pressure it caves to."