Some of the airline's staff reportedly made "malicious" postings on Facebook relating to planes flying out of Gatwick Airport.
The postings, which have now been removed, also reportedly included comments about passengers.
A Virgin Atlantic spokesperson said: "The airline has started an immediate disciplinary investigation.
"Virgin Atlantic does not tolerate any criticism of its passengers or industry-leading safety standards and is taking this matter very seriously.
"Safety is the airline's top priority and we operate our fleet of aircraft in strict compliance with all manufacturers' and safety authorities' recommendations and regulations."
The news comes as Virgin Atlantic continues its "No Way BA/AA" campaign, which was launched to fight the proposed merger between British Airways and American Airlines.
Virgin Atlantic, led by Sir Richard Branson, unveiled the 'Monster Monopoly' campaign website earlier this month, which outlines reasons why it believes the merger would be bad for consumers.
The launch was supported with an ad campaign in the national press.