Horan, 22, in a series of Tweets explained the ordeal he was put through.
"For the last two weeks I've been receiving messages off a group of fans, they have drowned my phone in messages, keeping me awake at night," he wrote.
He also expressed his anger at his family being targeted along with him.
"But the worst part is. They have been nothing but abusive. Saying things you wouldn't even believe about me and my family."
In response to messages of support from fans, he said he wanted to bring attention to the nasty messages because it happens to other people, and that he was okay.