Linton posted the picture of herself on Monday getting off a government plane in Kentucky with Mr Mnuchin.
In her post, the actress mentioned several designer labels for her all-white outfit, including Tom Ford and Valentino.
The commenter responded: “Glad we could pay for your little getaway. #deplorable.”
Linton responded on Instagram by calling the commenter “adorably out of touch”.
She suggested she and Mr Mnuchin, a former Goldman Sachs executive and hedge fund investor, contributed more to the US economy and paid more in taxes than her critic.
“Pretty sure the amount we sacrifice per year is a lot more than you’d be willing to sacrifice if the choice was yours,” she added.
She called the commenter’s response “passive aggressive” and “nasty” before ending her retort with a suggestion that the critic “go chill out and watch the new game of thrones”.
Linton’s Instagram account is private, but a screengrab of her response has circulated online.
The 36-year-old apologised last year amid criticism of a self-published memoir of a year she spent in Africa as a teenager, and withdrew the book.
Critics deemed it inaccurate in its depiction of life on the continent. An excerpt was published online by the Daily Telegraph, but taken down by the British newspaper “in light of the concerns raised by readers.”
Edinburgh-born Linton has appeared in movies including Cabin Fever, and TV shows such as CSI: NY, and more recently worked as a producer.
Mr Mnuchin produced several films before being tapped for the Treasury post by Donald Trump. The pair married in June in a ceremony attended by the president.