The airline, which is owned by Sir Richard Branson, opened an urgent investigation on Thursday night after the woman allegedly passed on information about eight celebrities to the Big Pictures agency.
The stars understood to be targeted include Hollywood actors Scarlett Johansson, Gwyneth Paltrow and Sienna Miller and singers Robbie Williams and Nicole Scherzinger.
Other high profile names whose flight details were accessed include Ashley Cole, the Chelsea and England footballer, his former wife and singer Cheryl Cole and Jermain Defoe, the Tottenham footballer.
The employee, reported to be a supervisor of Upper Class customers, quit after her alleged deal with the organisation was publicly exposed.
The airline was last night attempting to contact the celebrities and sources said an investigation had been launched to establish who could access its booking system. Officials were also urgently trawling the company's email archives.
Virgin Atlantic said it was taking the apparent leak "extremely seriously". Big Pictures is understood to have launched an investigation into affair.
It is understood the accused employee, who has not been named, denies the allegations, which stem from emails sent to her by agency staffers.
The emails were sent to the employee's private account in 2010.
The employee behind the apparent leak, who the newspaper declined to name, is understood to have told colleagues she was recently a victim of identity theft.
The employee, who held a relatively junior position, appears to have been told in an email from Big Pictures that the agency was "trying to sort you out some money with accounts".
According to The Guardian, Another email to Big Pictures reportedly says: "Got a few more for you!" then lists celebrity flights from London airports.
The employee, who looked after high-profile customers on Virgin Atlantic flights, said she was "not going to comment on that at all" before hanging up the phone on Wednesday.
On Thursday night, a Virgin Atlantic spokeswoman said: "The allegations that have been raised are extremely serious and we have launched an immediate investigation.
"The security of customer information is our highest priority and we have robust processes in place to ensure that passenger information is protected.
"The incident that has been alleged concerns eight customers' flights booked in 2010 and we are in contact with all of those people.â
She added: "It is too early to draw conclusions on this matter but of course we would deeply regret any concern that these allegations may cause the individuals involved."
Big Pictures was launched in 1992 by Australian photographer Darryn Lyons and claims to be the world's largest celebrity picture agency. A spokesman was unavailable for comment.
The allegations come as the Leveson Inquiry investigates methods of the British press.