"You are too complacent and will die quickly," one Chinese fan wrote on Horton's Instagram account.
Another said: "You are a loser for a lifetime because of your disrespect and the lose [sic] of the Olympic Spirit and international reputation.
"It can be a big shame on your whole country."
Other menacing comments levelled at Horton included 'Loser', 'Disgusting', 'B****', and 'Hate you'.
Horton refused to back down from his comments and told reporters he had no regrets about calling out Yang.
"I don't think it is a big statement because it is true, he has tested positive," he said.
"No athlete has really come forward and said it. It wouldn't have felt right if I raced against someone who had tested positive and didn't bring it up. Hopefully others will follow."
Yang reportedly tried to "taunt" Horton in the Rio training pool by splashing water at him last week.
The 20-year-old gold medalist launched a surprise chip at the controversial world champion when asked about the training incident.
"It got played up a bit but he splashed me to say hi and I ignored him, I don't have time or respect for drug cheats," Olympic debutant Horton said.
"He wasn't too happy about that so he kept splashing me and I just got in and did my thing."
After beating the Chinese swimmer by a very narrow margin, Horton said it wasn't Yang he had an issue with, but drug cheats in general.
"Definitely a win for the good guys," he said in a post race interview.
"I don't know if it's a rivalry between me and him, just me and athletes who have tested positive."
Horton clocked 3:41.55 seconds to claim the 400m title ahead of defending champion Yang, who swam a time of 3:41.68.
The 20-year-old is the first Australian since Ian Thorpe in 2004 to win the Olympic 400m freestyle crown.
"Welcome to the Australian 400m Olympic Champion Club! Well done mate!!" Thorpe tweeted.
Australian head coach Jacco Verhaeren threw his weight behind Horton's bold stance against drug cheats.
"To be honest everyone thinks the same way," he said.
"As a swimming organisation we have zero tolerance to drugs. It's the same as saying we don't like drug cheats."