Matheson is under pressure after admitting his teenage sons racked up the massive bill on his government owned iPad during a family holiday to Morocco.
This explanation came after the MSP initially denied any personal use of the device and blamed an out-of-date sim card.
The new Ipsos poll for STV News asked the public if they thought Matheson should keep his ministerial job or resign and the study found 61 per cent of people thought he should quit, with 31 per cent saying they think he should remain in post.
Asked about the findings at a health event, he said: “Look, I recognise some of the public concern around this matter and as I set out in parliament, as soon as I became aware that there had been use of my iPad for personal purposes, I took immediate action to ensure that parliament was fully reimbursed for that.”
Scottish Labour deputy leader Jackie Baillie said: "The verdict of the Scottish public is clear - they want a Health Minister focused on our NHS, not one focused on saving his job.
"Michael Matheson has misled the public and removed the focus from the ongoing and deadly crisis in our NHS. "It is time for him to step aside."