The accusation was made by former Labour MP Brian Wilson who said the last months of Mr Kennedy's life were disfigured by the “disgraceful” campaign pursued by the SNP.
Mr Wilson said Mr Blackford led a campaign that “unleashed a torrent of abuse” against the former Lib Dem leader.
Mr Kennedy lost his Ross, Skye and Lochaber seat to Mr Blackford in the 2015 General Election after a bitter and deeply unpleasant campaign. Shortly afterwards the former MP died in Fort William following his long battle against alcoholism.
Writing in The Times, Mr Wilson was responding to an interview with Mr Blackford carried by the newspaper at the weekend.
When questioned about the campaign, Mr Blackford said he was “proud” of the way the SNP conducted the campaign. He claimed to have no regrets when Mr Kennedy died claiming there was “absolutely no issue” between the Lib Dem and himself..
But Mr Wilson said: “Nobody has sought to draw a direct link between Charles's death and the behaviour of Mr Blackford and his supporters during the campaign. But what is beyond doubt is that the closing months of Charles's life were disfigured by a vendetta that was as disgraceful as it was unnecessary.
“As soon as Mr Blackford was selected as prospective SNP candidate in January 2015 he launched the hashtag `#Where'sCharlie?', which became dog-whistle politics that undoubtedly unleashed a torrent of abuse.
“Anyone paying attention knew exactly where Charlie was. He was battling alcoholism. He was mourning the death of his parents. He was grieving the early demise of his closest friend. He was desperate to spend time with his young son. And he still had a better Commons voting record than any SNP MP.”
Mr Blackford, a former senior executive at Deutsche Bank, had asked Mr Kennedy to “lay off” the personal attacks on him.
“With the benefit of hindsight, which is a wonderful thing, perhaps it would have been better not to do that, but that’s what happened and the Liberals have sought to characterise it in another way,” Mr Blackford told the newspaper.
Mr Blackford went on to claim that he was the victim of a “nasty” campaign.
He said: “I did not enjoy the election campaign in 2015 but that was more to do with the characterisation of me from the Liberals. I’m not in any way blaming Charles, who was the MP. It was the campaign against me. It was pretty nasty.”
Within days of Mr Blackford launching the “#Where'sCharlie?” hashtag, Mr Wilson said the chairman of the Skye SNP branch Brian Smith was tweeted about whether Charles “has a `problem' that stops you going to Westminster.”
According to Mr Wilson, Mr Smith bombarded social media and Mr Kennedy's constituency office with invective.
Replying to a tweet from the SNP MP Pete Wishart, Mr Smith once described Mr Kennedy as “our own arch-Quisling”.
A member of Mr Kennedy's staff worked full time to delete abuse from social media.
Mr Wilson said: “Mr Blackford, undisputed author of the `Where's Charlie?' campaign now invites us to believe that he had no knowledge of these activities and no power to call off the dogs. I don't believe him.”
Mr Blackford was unavailable for comment yesterday. But an SNP source said the police had not made contact with him or his campaign team. The source added: “The campaign did not make personal attacks – questioning an MP’s absences from Parliament over a 15-year period is wholly legitimate.”
Police Scotland said it received a report of a minor disturbance on the date of the incident but no offences were committed.