The U.S. Securities and Exchange Commission and other agencies are also investigating.
Regulators are examining whether Morgan Stanley, the lead underwriter for the IPO, selectively informed clients of an analyst's negative view of the company's prospects before the stock offering last week.
A Democratic aide to the Senate Banking Committee says the panel wants to know more about the IPO, and they're seeking to meet with Facebook representatives, regulatory agencies and others. The aide spoke on condition of anonymity because the committee's planned inquiry hasn't been publicly announced.
A group of shareholders have even filed a lawsuit, claiming there was a failure to disclose a drop in revenues at Facebook.
"If people with more power and money to invest got a different set of facts and information and analysis than the average retail investor, then yeah, that's troubling," said Jason Tanz, the senior business editor of Wired.
Facebook's stock is down almost 20 percent. Regulators are also asking whether the company sold 25 percent more stock than it originally reported to the public.
Facebook officials have not yet commented. Morgan Stanley says it followed the same procedures it uses with all IPOs.
The Associated Press contributed to this report.