The Scottish Professional Football League said it had contacted all member clubs to recommend they encourage the gesture at all fixtures as a "mark of respect for and to celebrate the life" of the former president of South Africa.
A minute's applause will also take place at all football matches in the Premier League, Football League and FA Cup, while FIFA said there would be a minute's silence as a mark of respect ahead of the next round of international football matches.
The International Olympic Committee has announced it will lower the Olympic flag for three days in memory of Mandela.
Sebastian Coe, chairman of the British Olympic Association and head of the London 2012 Games, said Mandela had been an inspiration.
Lord Coe said: "The values that are at the heart of sport - equality, opportunity and mutual understanding - are the very same values Nelson Mandela fought to instil and uphold. He lived his life with courage and conviction, and as we mourn his passing, we are grateful for the unending inspiration he has given us all." Other stars from the world of sport also paid tribute.
South African golfer Ernie Els hailed the former South African president as an "iconic leader".
"It is a very sad day, a very sad day for South Africa and the world," Els said. "He fought for what he believed in, went to prison for so many years and came out to lead our country. He was the father of our country and our continent."