A 74-year-old is accused of threatening Ms Freeman online, which she revealed has prompted heightened security measures.
The messages are believed to have followed the news of the deaths of two children - 10-year-old Milly Main and a three-year-old boy - from infections at the Queen Elizabeth University Hospital campus in Glasgow.
In an interview with Holyrood Magazine, the Cabinet Secretary said police officers have been stationed near her constituency office and she has had to step up her personal security.
She said: "I think the threats are a symptom of this notion that I am personally responsible for everything that happens.
"I cannot be personally responsible but I am accountable for how well our health service performs and how well I act to resolve those areas where it's not doing as it should do.
"This shouldn't be about me, it should always be about the care we deliver."
A police spokesman said: "Police Scotland has arrested and charged a 74-year-old man in connection with communications offences following a report that online threats were received by a member of the Scottish Parliament.
"The man appeared before Ayr Sheriff Court on Monday February 24 2020."
Ms Freeman also described a "heartbreaking" meeting with families of children getting treatment for cancer who had concerns about the safety of their ward in light of the infections.
She said: "Their account of their experience and the straightforward, perfectly legitimate questions they were asking about the safety of the environment, and therefore the safety of their child, were not being answered.
"That was genuinely heartbreaking for me because all I kept thinking was 'imagine your child has cancer and you do not know whether they're going to survive this or not' and you become, as they all have done, genuinely serious experts on the cancer that their child is suffering from, what that involves, what the treatment involves, and what they need to do to guard against infections.
"Your whole life shrinks to that focus, as it absolutely should, and here comes this other burden about whether this building where your child is being cared for is safe."