Vassar educated Kathryn Kalikow, along with her boyfriend Brian Whalen, advertised the drug for sale on the website Craigslist, New York police said.
Peter Kalikow, head of real estate firm H.J. Kalikow & Company, owned and published the Post from 1988 to 1994. He also is a former Port Authority commissioner.
Sources told the New York Daily News Tuesday that Whalen's family acknowledged their relative had become addicted to the drug and were trying to get him into rehab.
"It's an unfortunate situation (when) any young folks are involved in drugs," said Whalen's lawyer, Marvin Ray Raskin. "We are addressing the addiction issue as we speak."
The couple had been living in the Kalikow family's posh 5th Avenue penthouse at the time of their arrest. Kathryn Kalikow had been caring for her ailing mother, Mary.
In a brief statement, Peter Kalikow said the family was focused on getting Kathryn help.
"Mary and I are very concerned, and all we are concentrating on now is helping our daughter," Peter Kalikow said in a brief statement Monday.
They have both been charged with felony drug possession with intent to sell. They were released without bail.
2014: The Year in Fashion [PHOTOS]