Eduardo Bolsonaro, 35, told fellow lawmakers in the Chamber of Deputies that he had made the decision partly due to lack of support, adding that his father had not influenced his choice.
"It was a decision I had been thinking about for a long time," he told local media in Brasilia.
"You listen to the advice of many people. There is also the issue of my electorate. I confess that the majority was not supportive."
The president this week said Eduardo, his third son, could help "pacify" his Social Liberal Party (PSL) that is split by bitter divisions.
Bolsonaro, a close ally of US President Donald Trump, first said in July that his son was on track to becoming the ambassador in Washington.