The screen star dared Alex Salmond and Better Together leader Alistair Darling to be drenched in freezing water to raise money for charity.
Former chancellor Mr Darling completed the challenge on Friday and nominated his colleagues at the pro-Union campaign.
Mr Salmond nominated Prime Minister David Cameron as well as Deputy First Minister Nicola Sturgeon, who promptly accepted the challenge and was drenched herself.
The social media craze is aimed at raising awareness and money for the neurodegenerative disease ALS, or motor neurone disease.
Preparing for a soaking, Mr Salmond said: "I'd like to thank James McAvoy. It is for a great cause, motor neurone disease, and we should all be supporting it.
"But above all I get to make three other nominations. One is my deputy Nicola Sturgeon, because we're a team.
"Secondly I'd like to nominate every single member of the Scottish press corps, but I'll nominate (BBC Scotland political editor) Brian Taylor because he's the most experienced.
"And thirdly I'll nominate David Cameron, because I saw him in a wetsuit the other day so he's got the equipment."
The First Minister added "Here we go - go Scotland," before being drenched and joked "do it again" after the soaking.
Ms Sturgeon passed the challenge on to Deputy Prime Minister Nick Clegg, Scottish Labour leader Johann Lamont and Scottish Sports Minister Shona Robison.
In his ice bucket video, X-Men star McAvoy said: ''As it is the year of the Scottish referendum on independence, I'd like to nominate our political champions Alistair Darling and Alex Salmond to do their very worst. Alex, Alistair, you've got 24 hours.''
Mr Salmond earlier said: ''I'm always up for any challenge, and I'm game for this one.
''It will invigorate me for the next month of campaigning.''
Alongside pictures of his challenge, Mr Darling tweeted a link to www.gordonsfightback.com, an awareness-raising site set up by Better Together director of research Gordon Aikman, who has the disease.
Former US president George Bush, actress Gwyneth Paltrow and footballer David Beckham are among a host of well-known faces that have already taken the plunge.
Ms Sturgeon was nominated by Mr Aikman in his own ice bucket challenge, along with Scottish Conservative leader Ruth Davidson, deputy leader of Scottish Labour Anas Sarwar and co-convenor of the Scottish Greens Patrick Harvie.
Ms Davidson and Mr Sarwar have both posted videos of themselves taking up the challenge on Twitter.