Ruby Rai, 17, ranked first in the Bihar state exams - but said in a video interview that her main subject political science was about cooking.
After the video went viral, Ms Rai was made to re-sit her exams, and was arrested after she failed and had her original results cancelled.
She was produced in court on Sunday where a magistrate sent her to jail until 8 July.
The decision to send her to prison has been criticised given that she is a minor and should, therefore, be sent to a detention home for juveniles.
The Hindu newspaper quoted Senior Superintendent of Police Manu Maharaj as saying that Ms Rai would have to "prove" that she was a minor. He did not specify how.
One state minister told reporters that authorities needed to make the system accountable instead of punishing students.
Meanwhile, arrest warrants have been issued for several other students who performed well in the exams, including Saurabh Shrestha who topped the science stream, but later could not say that H2O was water.
The AFP news agency quoted police as saying that another 18 people had been arrested.
Examiners who retested Ms Rai told reporters they were "shocked" by her performance. When asked to write an essay about the Indian poet Tulsidas, she only wrote "Tulsidas ji pranam (Salutations to Tulsidas)".
Last year, parents of students in the state were photographed climbing school walls to pass on answers.
The embarrassed state government had announced tough measures like fines and jail terms, intended to curb cheating this year.
The markedly lower pass rate seen in the results announced last month was taken as an indication that the steps had worked.
That is, of course, until the footage of Ms Rai's interview was aired.
An Indian student has been sent to jail for cheating after she failed a retest.