James Dornan made the comment after Ms Smith, who was appointed BBC North America editor last year, told of her relief at leaving the "bile and hatred" of Scottish politics for a new role in the US.
She said she was "demonised quite heavily" among parts of the population following the independence referendum, and worried the "criticism, bile and hatred" she attracted from some quarters was damaging the reputation of the BBC.
In an interview with Rhys Evans, head of corporate affairs at BBC Wales, for a paper on news coverage in a "multinational state", Ms Smith spoke of "deeply unpleasant" abuse aggravated by her gender.
People would “...roll their car windows down as they drive past me in the street to ask me, ‘What f****** lies you're going to be telling on TV tonight, you f****** lying b****?'" she said.
She said she felt "relief" at leaving Scotland for the US, where she will be “gloriously anonymous”.
She added: “Nobody will have any idea who my father is. So, the misogynistic idea that I can't have any of my own thoughts anyway, or rise above my family connections to report impartially will no longer be part of the discourse.”
In response to a tweet about the story, Mr Dornan wrote: “America would be the go to place to escape all her imaginary woes then.”
Scottish Conservative MSP Annie Wells branded his comment “appalling”.
Writing on Twitter, Mr Dornan said: “Language is important in this so I apologise for my earlier comments that made it seem as though I believed the abuse Sarah Smith has suffered was imaginary.
"No matter differing opinions, the misogynistic abuse of women in the public eye is never acceptable.
“If we want to tackle the issue then we all need to recognise the problem is on all sides and all countries.”