Hill, 22, said in a statement that he would not be competing in the rest of the European Formula Three season because he wanted to pursue other interests.
"Coming from the Hill family it was inevitable that I would be drawn to racing. I have learned an enormous amount and really enjoyed the experience, but I do not want to compete unless I am 100 percent devoted," he said.
"As I now have ambitions in other fields I feel it is the right move to withdraw from racing."
Damon Hill was world champion in 1996 while Graham, who died in a plane crash in 1975, took titles in 1962 and 1968. They are the only father and son to have won the Formula One championship.
Josh Hill, whose website (www.joshhillracing.net) states his 'burning ambition' of becoming the first third generation F1 champion, had been competing in what was previously the F3 Euro Series that served as a stepping stone for champions Lewis Hamilton and Sebastian Vettel.
His best result was second at Hockenheim in May.
"Being born into a racing dynasty is not something many of us can easily relate to," said Damon Hill. "It is entirely understandable if Josh has to find out if racing is his main calling or not.
"So it is with some sadness that we make this announcement. I'm sure there will be many disappointed Hill' fans out there but we hope they will be understanding...It is sometimes braver to stop than to carry on. He has my total support as always."
(Reporting by Alan Baldwin; Editing by John Mehaffey)
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