The article, published on The Cut website, also claimed that Nick shares a "fraudulent relationship against his will".
"I want to sincerely apologise to Priyanka Chopra, Nick Jonas, and to the readers I offended and hurt with my words. I do not condone racism, xenophobia, or sexism. I take full responsibility for what I wrote, and I was wrong. I am truly sorry," Smith posted on Twitter.
The article was slammed online by many people, including Nick's brother Joe Jonas and his fiancee, Game of Thrones star, Sophie Turner. The duo attended the wedding in Jodhpur along with the rest of the family members.
One of the sentences of the article was, "All Nick wanted was a possible fling with Hollywood's latest It Woman, but instead he wound up staring straight at a life sentence with a global scam artist."
"Even more upsetting, she's a scam artist who never even took the time to make sure he was comfortable riding a horse before arranging for him to enter their wedding ceremony on horseback," Smith had written.
After the furore, the website issued an apology and said it has deleted the objectionable article.