Lew said Wednesday that a woman's face would appear on the $10 bill in 2020, in time for the 100th anniversary of the passage of the 19th Amendment, which gave women the right to vote.
But he also said Hamilton will not disappear entirely from the bill. The nation's first Treasury secretary will either appear with the woman on the $10 bill, or two separate bills will be issued.
Bernanke said the decision to honor a woman on the $10 bill is a "fine idea," but shouldn't come at Hamilton's expense.
On his blog, he listed several of Hamilton's accomplishments, such as founding the nation's first major bank, the Bank of New York, his 1791 Report on the Mint, which set the basis for U.S. currency arrangements, and his role in establishing the modern U.S. economy.
Bernanke called for an alternative, which was already widely discussed on social media -- remove Andrew Jackson from the $20 bill instead.
Calling him a "man of many unattractive qualities," as well as a "poor president," Bernanke said Jackson would "probably be fine with having his image dropped from a Federal Reserve note" based on his opposition to central banking.
Bernanke called the option of circulating two versions of the $10 bill "less attractive."
"The Treasury Department should do everything within its power to defend the honor of Jack Lew's most illustrious predecessor," Bernanke wrote on his blog.
The public can submit suggestions at thenew10.treasury.gov or through social media by using the hashtag #thenew10. Lew will announce his selection at the end of the year.