Last month, Obama -- speaking on the economy at a factory in Wisconsin -- said "folks can make a lot more, potentially, with skilled manufacturing or the trades than they might with an art history degree."
The US leader immediately added, to laughter from the crowd: "Now, nothing wrong with an art history degree -- I love art history. So I don't want to get a bunch of emails from everybody."
But Ann Collins Johns, an art history professor at the University of Texas in Austin, did feel insulted, and she registered her protest via the White House website.
She got the shock of her life several days later -- a response from the commander-in-chief himself.
"Let me apologize for my off-the-cuff remarks. I was making a point about the jobs market, not the value of art history," read the letter.
"As it so happens, art history was one of my favorite subjects in high school," it added.
The White House sent Johns a scan of the handwritten note via email, with the original to follow by regular post.
A copy of Obama's note was published on the arts blog hyperallergic.com. Contacted by AFP, the White House did not dispute the authenticity of the note, but did not offer additional comment.
Johns said she was very surprised to get such a response from a president she already admired.
"So now I'm totally guilty about wasting his time," she said, according to the blog.