The texts read: "I wouldn't rent it to u if u were the last person on earth" and "One word says it all. Asian."
The host said: "It's why we have Trump... and I will not allow this country to be told what to do by foreigners."
Ms Suh, an American citizen though it was hardly relevant in the case, recounted the experience in a YouTube video posted in April.
"It stings that after living in the US for over 23 years this is what happens. No matter if I follow the law... no matter how well I treat others, it doesn't matter. If you are Asian, you're less than human and people can treat you like trash," Ms Suh, who worked as a law clerk at the Riverside County Public Defence's Office, said in the video.
After Dyne Suh filed complains to Airbnb, the accommodation sharing service provider carried out investigation and banned Barker from the platform.
Ms Suh also complained to the California Department of Fzair Employment and Housing (DFEH), which ordered Barker to make a personal apology to Ms Suh, pay a $5,000 fine and take an Asian American studies course.
Airbnb, which is headquartered in San Francisco, reached an agreement with the DFEH in April which allows the regulator to test and penalise Airbnb hosts for racial bias. Barker is the first Airbnb host that has been punished under the agreement.
Airbnb gave in to the DFEH's demand after researches and a growing number of reports suggested hosts regularly refuse guests due to their race, a problem exposed in 2016 under the hashtag #AirbnbWhileBlack.