In a short statement issued on Wednesday, Schumer said, "I consider Senator Franken a dear friend and greatly respect his accomplishments, but he has a higher obligation to his constituents and the Senate, and he should step down immediately".
Mark Dayton is now mulling a replacement.
Republicans are eager to recapture a seat that Franken won in 2008 by a tiny margin and only after a monthslong recount.
Franken's resignation comes a day after many of his fellow Democratic senators - including New York's Kristen Gillibrand, California's Kamala Harris, Ohio's Sherrod Brown and Missouri's Claire McCaskill - called upon Franken to step down from his role on Wednesday.
Hours later, another woman said Mr Franken inappropriately squeezed "a handful of flesh" on her waist while posing for a photo with her in 2009. I think that was the right thing to do. The woman, Stephanie Kemplin, said Franken cupped her breast while she was deployed in the Middle East during the Iraq War.
Former Sen. Norm Coleman, who served one term before losing to Franken, quickly announced he would not run in 2018, but other candidates could emerge.
Pawlenty now serves as CEO of the Financial Services Roundtable, a Washington lobbying group, and is considered a good bet to raise a lot of money quickly. The position with the leading financial services lobbying group in Washington has kept him close to national tax and monetary policy, including the GOP-controlled Congress' tax plans this year. There is "irony in the fact that I'm leaving", Franken said, when Trump is not and Roy Moore "campaigns for the Senate with the full support of his party". Republicans hold a 52-48 majority in the Senate.
Pawlenty did not return calls seeking comment. It would be highly irregular for the liberal politician to appoint a Republican to the seat.
Democrats' hopes in Minnesota could ride on someone shifting out of next year's race for governor. The name most often mentioned is Lt. Gov. Tina Smith. She's known largely for behind-the-scenes work, including as Dayton's former chief of staff. She also served as a top executive at Planned Parenthood in Minnesota, North Dakota and South Dakota. Most expect Franken will announce his resignation at that time. Jeff Sessions' was appointed attorney general.
"I know in my heart that nothing I have done as a Senator - nothing - has brought dishonor on this institution", he added, noting he was shocked at the allegations against him, and painting himself as "a champion of women". Franken has said that he will be making an announcement about his political future tomorrow.