The 32-year-old guard shared an image on Chinese social media outlet Weibo of his graffiti, saying "Had a blast at the Great Wall of China today."
Brown and his Houston teammates visited the historic landmark during a trip to China with the New Orleans Pelicans for the NBA's Global Games China.
The post, later deleted, launched an onslaught of critical remarks.
Brown apologized for his actions.
"We were out enjoying the Great Wall," he said. "I never (had) been, it was my first time. I wrote my name on the wall in chalk. I saw different writings -- I didn't mean any harm by it. I made a mistake. I could have just put my hand over it and erased it. It will never happen again. I've been playing in China for three years now and I have the utmost respect for the Chinese culture, and the way of living here. I pretty much adapted, coming from the States, here for three years. My teammates, the fans in Shenzhen and the fans all over were great to me, and I just want to sincerely apologize for that."
Brown has played the last five seasons overseas -- including three in China -- and is battling for a roster spot with the Rockets. He last played in the NBA for the Los Angeles Clippers in 2010.