Obama criticized such offshore accounts when he campaigned for re-election last year. But the White House said the investment should not get in the way of Lew's confirmation, given that it was already known when he was confirmed for two other government positions, including White House budget chief.
Lew told the committee he did not initially know his investment was registered in the Cayman Islands and said he did not receive any tax benefit from the investment and sold at a loss.
Hatch and others also said they will ask Lew about his knowledge of financial markets, where Lew has admitted to a lack of experience, despite his time at Citigroup.
The Treasury secretary serves as chair of the Financial Stability Oversight Council, a panel of banking and market regulators that is close to imposing additional rules on a handful of large, complex financial institutions meant to ensure they do not threaten the stability of the financial system.
(Read More: What's Lew's to Do at Treasury?)
Lew lacks the international stature of his predecessor, Timothy Geithner, who had met regulators from around the world as president of the New York Federal Reserve Bank and was a senior financial diplomat in a prior stint at the Treasury.
(Read More: What Would You Call Tim Geithner's Book?)
Lew served as deputy secretary of state under Hilary Clinton, but his main responsibility there was managing the State Department's resources.
His real passion is for budgets. He worked as the White House budget chief twice, first under President Bill Clinton.
"Budgets aren't books of numbers. They're a tapestry, the fabric, of what we believe," he told Congress in 2010.
Analysts said the choice of Lew as the administration's top economic official signals the importance Obama places on ongoing battles in Washington over the government's budget.
If confirmed, Lew will take the helm at Treasury as the White House heads into another round of difficult talks with Congress on how to put the United States on a sound fiscal footing. (Read More: Obama Looks for 'Big Deal' on Spending Cuts and Taxes)
Senate Democrats are expected this week to reveal a series of targeted spending cuts and tax increases on high earners to replace across-the-board federal spending cuts due to kick in on March 1. Senate Republicans are likely to reject any proposal that includes tax hikes.
)In his opening remarks, Lew spoke out strongly against allowing the automatic cuts to take place on March 1, saying they would impose "self-inflicted wounds" on a fragile economic recovery.