Radio DJ Horobin, 32, apparently cheated on her husband with the singer when he was 17 last year.
Horobin has subsequently suffered tirades of abuse on Twitter, being branded "sick" and a "whore" by Styles admirers.
Lucy Horobin, who left a sad smiley face shortly after the news broke, thanked followers for their support.
She wrote: "To clarify, I haven't said ANYTHING to any press, nor do I wish to. Thank you to those of you who have said kind words today. Xxx"
Harry Styles has chosen not to discuss the rumours on the social networking site, instead referring to a "fun show" in Dallas.
Their relationship allegedly took place before he began dating Xtra Factor presenter Caroline Flack, also 32.
Styles, now 18, has previously denied suggestions that he is only interested in older women.