The 5th U.S. Circuit Court of Appeals in New Orleans delayed the report date Monday to allow the court time to consider a request for bail while Skilling appeals his conviction.
Skilling was to have begun serving his sentence Tuesday in a federal prison in Waseca, Minn.
The appeals court said in a docket entry on the court's Web site that the delay was "solely to allow this court to give careful consideration to the request for bail pending appeal." According to the entry, a new report date would be set pending further court order.
Skilling's defense attorney did not immediately return a message seeking comment.
Skilling is the highest-ranking executive to be punished for the accounting tricks and shady business deals that led to the loss of thousands of jobs, more than $60 billion in Enron stock and more than $2 billion in employee pension plans after the company imploded in 2001.
He was convicted along with Enron founder Kenneth Lay in May. Lay died of a heart attack in July in Aspen, Colo., and his conviction was vacated.
Skilling planned to undergo alcohol and mental health counseling at Waseca, successful completion of which could shave a year off his sentence. He would also be eligible to earn 54 days a year off his sentence for good behavior.
The low-security prison sits on the city limits of Waseca, a town of 8,400 people 75 miles south of Minneapolis.
The site was a branch campus of the University of Minnesota until 1992, when it was shuttered in a round of cost cutbacks. City officials hoping to save much-needed jobs approached federal authorities and suggested it as a prison, and today the 80-acre facility houses 1,070 federal inmates.
Most inmates were lower-level players in the drug trade, according to Felicia Ponce, a spokeswoman for the Federal Bureau of Prisons. She said Skilling likely wouldn't be among many other white-collar criminals.