The DVD recording of Chua and a woman he described as a "personal friend" had been circulating in Malaysia for more than a week.
In comments before his resignation was announced, Chua said he did not make the video but it remains unclear how it came into existence.
"I would like to emphasize that I did not make the tape myself. Who has done this and why it was done is obvious. Who made this tape is not important any more," he said, apparently suggesting it was made by his political rivals.
The tape was apparently made on a CCTV camera in a hotel room.
The scandal was seen as a major embarrassment to Abdullah Badawi, the Malaysian prime minister, who has been expected to call snap elections in the coming days.
Chua is also vice president of the Malaysian Chinese Association, the dominant ethnic Chinese party in the ruling coalition.
He had earlier said he would not resign, saying the decision on his future lay with the prime minister.