The northern state's governor Mark Dayton appointed Lieutenant Governor Tina Smith to fill Franken's seat, almost a week after the comedian-turned-politician announced his resignation in the face of multiple accusations of sexual misconduct.
Smith promised to make the battle against sexual harassment a key issue during her tenure, but sidestepped a question about whether President Donald Trump should resign or be investigated over claims that he has acted inappropriately.
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"We are in the middle of a sort of sea change in attitudes about this right now," Smith told a press conference in St Paul, the state capital of Minnesota.
"I can promise you that I will be working on these issues when I get to Washington."
Smith's appointment will not alter the power dynamic in Washington, for now.
But it will keep the Republican majority in the Senate at 51-49 seats, following an upset Tuesday in Alabama in which a Democrat was elected for the first time in 25 years in the deeply conservative state.
Smith also promised to run to keep the seat in next year's midterm elections, during which Democrats will seek to upend the Republican majority.
Outgoing senator Al Franken backed the appointment, tweeting "Tina Smith will make an excellent United States Senator".