Prosecutors filed the appeal Friday, questioning the sentence imposed on Stacey Dean Rambold, who pleaded guilty to raping a 14-year-old girl, was released in September and is serving probation, CNN reported.
Prosecutors said the 10-year-prison sentence they sought at trial still would be appropriate.
"The circumstance of a 47-year-old teacher having sexual intercourse with his 14-year-old student is precisely such a circumstance warranting a mandatory minimum sentence," the filing said.
The appeal -- filed with the Montana Supreme Court -- cites remarks by District Judge G. Todd Baugh, who said in imposing the sentence the victim "seemed older than her chronological age."
Baugh has said he erred in his original ruling and tried to revisit his sentence in September, but the state Supreme Court barred him from making a new ruling because he didn't have standing to change the sentence.
CNN said it wasn't clear when the appeal would be answered.
Baugh has tried to apologize for his statements, calling them demeaning to women and not relevant to the sentencing -- and saying they do not reflect his own beliefs.
Rambold was charged in 2008 with three counts of sexual intercourse without consent. The victim killed herself in 2010.