The BBC comedy last aired on Christmas Day in 1978.
The sketch reunites Crawford, 74, with on-screen wife Betty (Michele Dotrice), and features an appearance from Olympic cyclist Sir Bradley Wiggins, leading to one of Frank's typical disasters.
"I am thrilled and delighted to have been asked to bring Frank back," he said.
Dotrice said it would be an "absolute joy to be reunited again with Frank" and that it was fitting "for it is such a wonderful cause".
Sir Bradley added: "I am a huge fan of Michael so it's an absolute honour to be asked to be involved alongside such an icon of British television... and all for a great cause."
When the show wrapped in 1978, Crawford went on to star in the original production of The Phantom of the Opera and other successful Andrew Lloyd Webber productions such as The Wizard Of Oz.
Sport Relief Night airs on BBC One on 18 March from 19:00 GMT.
Michael Crawford is set to reprise the role of Frank Spencer in a one-off special of Some Mothers Do 'Ave 'Em.