More than 100 Ukrainian journalists have written to President Viktor Yushchenko demanding he apologise for labelling a reporter a "hitman".
Viktor Yushchenko (R) said his family had a right to privacy
Serhiy Leshchenko had pressed the president to answer questions about his son's spending and lifestyle.
Andriy Yushchenko is a 19-year-old university student, but reportedly drives a BMW worth $120,000 (£70,000).
The row has strained relations between the president and the same press that supported his "orange revolution".
It suggests the honeymoon between President Yushchenko and the press may be over, says BBC world media correspondent Sebastian Usher.
Mr Leshchenko, a reporter with the widely read online newspaper Ukrayinska Pravda, has written articles questioning how Mr Yushchenko's son could support his apparently lavish lifestyle.
The president said his son had a job that allowed him to rent the BMW M6 sports car, and that an expensive mobile phone he uses was a present from a friend.
When the reporter asked on Monday where the boy worked, Mr Yushchenko told him to "act like a polite journalist and not like a hitman".
Andriy Yushchenko is said to drive a BMW M6
The response outraged journalists, who accused the president of returning Ukraine to the climate of censorship experienced under his predecessor, Leonid Kuchma.
"We don't think that the vocabulary and the tone that you used while answering a question about your son's lifestyle are worthy of a leader of a democratic European country," said a letter signed by more than 100 journalists and posted on the Ukrayinska Pravda site.
"You have to realise that you and your family are objects of public attention. Society has the full right to know about the revenues, spending and lifestyle of your family," it continued.
Mr Yushchenko replied with his own open letter, saying: "It's right for the president's family to live under the press spotlight.
"But it's not a reason to deny my family the right to a personal life."