Responding to Tory MSP Brian Whittle at First Minister's Questions, Nicola Sturgeon said "more needs to be done" on the issue.
Mr Whittle asked: "Does the First Minister agree with HIV Scotland... that it's time for a public campaign to end public stigma?"
Ms Sturgeon argued there could be cause for a public push, following the roll-out of anti-HIV drug PrEP, which is designed to prevent contraction of the condition in the first place.
She said: "There's an argument for a campaign, particularly given the successful introduction of PrEP, and we will continue to consider what work we can do to ensure we are consigning this horrible stigma that wrecks people's lives to the dustbin of history, and I'm sure that's something we will all come together to do."
Both the First Minister and Mr Whittle also praised former Welsh rugby player Gareth Thomas, who recently revealed he has the disease.
She said: "I think his brave and emotional intervention will have done a great deal to address the stigma here, and a lot of people across the UK and further afield owe him a debt of gratitude.
"I'm sure we all send him our very best wishes."
Thomas revealed his diagnosis at the weekend, saying he was doing so himself after a tabloid threatened to publish the news.
In a video on his Twitter account, Mr Thomas said he wanted to show not all people with HIV are "close to dying".