In a statement sent to The Associated Press, the Forum said its board - which includes former US Vice President Al Gore, Jordan's Queen Rania and European Central Bank President Christine Lagarde as members - agreed to a decision by its risk and audit committee to open the probe.
"While the Forum takes these allegations seriously, it emphasises that they remain unproven, and will await the outcome of the investigation to comment further," the statement said.
The AP was not immediately able to reach Schwab or a contact person for him.
The allegations emerged two days after the WEF announced Schwab had retired "with immediate effect" as chairman, and that former Nestle Chairman and CEO Peter Brabeck-Letmathe was taking over as interim chairman.
For decades, the Forum's annual gathering in Davos has hosted top business executives, government leaders, academics, international organisations, cultural figures, sports legends and celebrities to discuss government policy, deal-making and current affairs. (AP) SCY SCY