Robinson, 51, was vilified online by Yes campaigners before the September referendum last year, who attacked him for what they saw as an anti-independence slant to his coverage.
Protesters even carried a large poster calling for his dismissal as BBC political editor during a demonstration outside the BBC's Scottish headquarters in Glasgow.
Last week, Robinson revealed he was having an operation to remove a bronchial carcinoid tumour from his lung.
Amid an avalanche of people tweeting best wishes for a full recovery, a handful claimed his cancer was "karma".
The user had "45" in their Twitter handle, a reference to the post-referendum movement that pledged to continue campaigning for independence.
The user's tweets are now protected but not before the original comment was re-tweeted:
Calling the tumour "karma" was a popular theme:
@Holbornlolz, who claims to be "Britain's most vile troll" and tries to test boundaries with particularly bad taste tweets, said:
Every single Political Leader had to have Nick Robinson surgically removed from their arseholes.
Karma strikes.— Old Holborn (@Holbornlolz) February 28, 2015
Another "45" tweeter, whose account is now also protected, tweeted: "A bit of chemotherapy would do the biased beeb man good".
David Cameron tweeted Robinson his best wishes and a "speedy return for the general election", prompting one Cybernat to reply:
A spokesman for the Scottish Conservatives told The Telegraph: "These comments are despicable, but won't surprise anyone who saw the depths some people stooped to during the referendum campaign.
"It's important all political parties lead by example and condemn this sort of behaviour."
Robinson has not acknowledged the abuse but tweeted thanks to the well-wishers and said he "hoped to be back reporting the news soon".
Thank you for the many kind and generous messages. Here's hoping to be back reporting the news soon— Nick Robinson (@bbcnickrobinson) February 28, 2015
Scotland's First Minister Nicola Sturgeon tweeted her best wishes to Robinson.
.@bbcnickrobinson best wishes for a speedy recovery.— Nicola Sturgeon (@NicolaSturgeon) February 28, 2015
In September, when Sturgeon was deputy first minister, she criticised the SNP supporters who demonstrated outside the BBC and called for Robinson's sacking, saying: "We should spend every moment of those three days not protesting against something but campaigning for something, for a yes vote to give us the power to transform our country.”
This was in contrast to then SNP leader Alex Salmond, who said of the same protest: ""I think there is a real public concern, in terms of some of the nature and balance of the coverage.
"You must allow people to express a view in a peaceful and joyous fashion. That is part of the democratic aspect of politics."