The suspect has spent 15 months remanded in custody, having been arrested in January 2016.
The girl is accused by the prosecutor of planning terror attacks against two schools – the girl's previous school, Sydskolen in Fårevejle, western Zealand; and a Jewish school in Copenhagen. She denies the charges.
Manuals on how to make bombs and prepare explosives were found when the girl, then 15, was arrested last year, reports news agency Ritzau.
State prosecution has now accused the girl of terrorism.
The trial will begin in front of a jury at Holbæk court on Wednesday, reports Ritzau, with the girl now having spent 15 months in custody.
She will be the first female in Denmark to go on trial for terrorism offences.
Sydskolen had reported the girl to police prior to her arrest in January last year, after several of the school's students expressed their concerns to teachers over statements made by the girl on social media.
The girl was waiting for orders before carrying out her alleged attack on Sydskolen, reports Ritzau, and was also arrested before making her alleged attacked on Carolineskolen, a Jewish private school in Copenhagen.
Shortly after her arrest last year, the girl was described as a recent convert to Islam and one of her neighbours told tabloid BT that her Facebook page indicated that she wanted to convert other Danes to the religion.
TV2 also reported that the girl's profile page indicated that she was a member of a Facebook group for ethnic Danish members of Hizb ut-Tahrir, an Islamic group that supports the establishment of a caliphate and that has been at the centre of numerous controversies in Denmark.
A 24-year-old man who had previously fought alongside extremists in Syria was also arrested and detained in January 2016 in connection to the case. The alleged jihadist was described as “a friend” of the teenage girl.
Senior prosecutor Kristian Kirk told Ritzau that the Kundby girl case was “completely unusual”.
“Firstly, the nature of the case – it's a very serious charge. Schools and children were the targets,” Kirk said.
“Furthermore, at the time of the crime the girl was 15 years old, a teenager from western Zealand and unknown to police. Thirdly, we have the movement for custody,” the prosecutor added.
The prosecution says that the girl is considered to be so dangerous that she should be kept in custody indefinitely, reports Ritzau.
“It is very unusual that we move for something like this for such a young person with no criminal record,” Kirk said.
According to Danish law, a person can be imprisoned indefinitely if found guilty of a very serious crime and judged to be a risk to society.
Defence lawyer Mette Grith Stage told the news agency that she was surprised by the calls for such a strong punishment for a “young girl”.
“It is clear that my client is both shocked and scared by the punishment advocated. It is a difficult thing to have hanging over one's head,” she said.
A verdict in the case is expected in May.