The public broadcaster complained about 13 videos uploaded to indy website Wings Over Scotland, with the channel subsequently closed.
Stuart Campbell, who runs Wings Over Scotland, has claimed his YouTube channel was shut without warning.
Peter Curran also separately had his pro-independence channel closed following BBC copyright complaints. Mr Campbell has claimed the videos should not have been removed.
In a letter to BBC chief Tony Hall, the former First Minister has demanded the corporation prove it “is not pursuing a campaign against sites which support Scottish independence”.
Salmond said his concern over the legal action was in part because one of the videos on the blog was an interview with him in the run up to the 2014 independence referendum.
Salmond also claimed the corporation refused to take part in an interview on the issue on the BBC’s Good Morning Scotland programme yesterday.
In the letter obtained by the National newspaper, the former politician asks the Baron Hall of Birkenehead to explain why “popular independence-supporting websites [are being] targeted for enforcement action by the BBC lawyers in London” while “Unionist-supporting sites” have been allowed to keep “innumerable BBC excerpts in use on YouTube channels”.
He continues: “If memory serves, this news interview now removed from YouTube was a challenge from me to the then prime minister to debate on Scottish independence. It has now disappeared from the public record thanks to the BBC action.”
Salmond adds: “Why does the BBC as a public service broadcaster presume to effectively expunge my interview from the public record without so much as a by-your-leave?”
He concludes: “There is a considerable public interest in this matter and I look forward to an early reply and hopefully one that satisifies the Scottish public that the BBC as a public service broadcaster has not set its face against fair comment and freedom of speech and further is not pursuing a campaign against sites which support Scottish independence.”
The BBC has reportedly denied being selective in its actions to protect copyright.
The broadcaster has said it takes action to protect its copyright “whenever we receive complaints about large volumes of our material being posted or used without authorisation”.
A BBC spokesperson told The Scotsman on Monday: “This action is normally limited to asking for individual videos to be removed and the BBC did not ask or demand for these whole channels to be taken down.
“That was a decision for YouTube alone.
“We act irrespective of the political views of the infringing YouTube channels and have taken action against the use of our material by individuals or organisations from across the political spectrum.
“There is a standard process in place if these channels wish to challenge the take down orders and we will consider any representations carefully.”
Mr Campbell launched a scathing attack at the BBC yesterday, saying the public broadcaster have operated “a plainly partisan policy, observably applying different rules and procedures to people with different political viewpoints.”