The audio recording of Yair Netanyahu, who has been the subject of controversy in the past, was aired by Israel's Channel 2 television late Monday.
On the recording, said to be from 2015, Yair Netanyahu, now 26, can be heard speaking with the son of Kobi Maimon, a stakeholder in a company that owns a share in Israel's offshore Tamar gas field.
Their conversation includes talk of strippers and prostitutes.
"My dad arranged $20 billion for your dad -- you can give me 400 shekels ($116/97 euros)," he says.
Yair Netanyahu issued a statement apologising and saying he was only joking about the gas deal while "under the influence of alcohol".
"These statements do not represent who I am nor the values on which I was raised," he said.
"Regarding what I said about the gas deal, it was a joke. Anyone with a bit of common sense understands that right way."
Netanyahu faced a difficult political battle over Israel's natural gas arrangements, with opponents saying they overly favour the companies involved.
Labour party leader Avi Gabbay said the recording was a "new stain on the corrupt gas deal."
There was also criticism over Yair Netanyahu's security arrangements. A security guard employed by the state purportedly accompanied Yair Netanyahu to the strip club.
Netanyahu's office said it "is not consulted on protection arrangements for his children decided upon by the security services."
The Netanyahus' in a statement denounced the broadcast of the recording, saying it was part of a "witch-hunt against the family that has reached an unprecedented low."
"Apparently, everything is fair game to attack the Netanyahu government and family, including using a secret and illegal recording of young men drinking alcohol."
