Horton was the target of online abuse just hours after taking home the gold medal in the men's 400m freestyle final over comments he made calling Chinese runner-up Sun Yang a "drug cheat".
The Chinese swim team issued a statement, calling Horton's claims a "malicious personal attack" on Yang.
"We have been noticing what has been said in the past two days by Horton, who launched a malicious personal attack [on Chinese swimmers]," team manager Xu Qi told China's state-run Xinhua news agency.
"We think his inappropriate words greatly hurt the feelings between Chinese and Australian swimmers. It is proof of a lack of good manners and upbringing.
"We strongly demand an apology from this swimmer."
Yang fired shots back at Horton a day after the Australian's gold medal-winning swim.
When asked if he would beat Horton in the 1,500m, Yang told Channel 7: "In 1,500m I am the king."
Horton and Yang will face off again in the men's 1,500m freestyle event on Sunday.