An apologetic Minami Minegishi, 20, appeared in a YouTube video with her haircut to show remorse and regret, accepting blame for the situation with 19-year-old boyband member Alan Shirahama and begging to be allowed to remain with the group.
The scandal came about when Minegishi was seen leaving Shirahama's apartment. AKB48 - which has around 90 members, all female - bans everyone from dating.
According to AFP, members are prohibited from embarking on a relationship in order to keep the male fans happy.
AKB48 are also known for using sex appeal to promote their music, often dressing provocatively.
Minegishi told AKB48 fans on YouTube: "[The tryst was] thoughtless and immature.
"If it is possible, I wish from the bottom of my heart to stay in the band. Everything I did is entirely my fault. I am so sorry."
The video has received more than four million hits on YouTube since it was posted yesterday (January 31).