"That was one of the reasons," Zia told a news conference. "A controversy was created for no reason. And I know my son is a very sensitive boy and he was under pressure as a cricketer because of my position."
Medium-quick bowler Junaid Zia was a surprise selection for Pakistan's home one-day series against Bangladesh in September, when he took three wickets in four matches.
The 19-year-old was also selected for the current one-day series against New Zealand but withdrew 24 hours later.
Zia, a 57-year-old retired army general, said he was confident his son would be able to win a place in the team without accusations of nepotism following his resignation.
"But let me make it clear my decision to step down was not an emotional one. I thought long and hard about it and consulted my family," Zia added.
Junaid Zia was in Pakistan's under-19 World Cup squad last year but has only played six first-class games.
His father had been widely expected to resign earlier this year following Pakistan's poor World Cup performance.
Zia offered to quit last year after Pakistan were bowled out for their lowest test scores (53 and 59) in a test match in Sharjah against Australia but Pakistan President Pervez Musharraf, the cricket board's patron and a close friend, asked him to carry on.
Zia, in charge since November 1999, said he had recommended chief executive Ramiz Raja as his successor.