The school girls were arrested east of the capital Addis Ababa and first appeared in court last month alongside an 18-year-old woman.
They are accused of handing out Christian books, written in Arabic.
Ethiopia:
- Population: 101.9 million, 63.8 million Christians
- Main Religion: Christianity (mainly Orthodox), Muslim
- Government: Federal republic
- World Watch List Rank: 18
- Source of Persecution: Islamic extremism/ Denominational elitism
Some Muslims said the book is an insult to Islam and last month a group attacked the Protestant Meserete Kristos Church.
The church has apologised for the book being distributed.
Eden, 15, Gifti, and Mihiret, both 14, were then kept in custody after the police asked for more time to investigate the claims.
Earlier in October the girls were taken to be examined by a doctor to determine their ages - there is no official birth certificate process in Ethiopia.
There have been accusations that the girls have suffered violence in prison.
Their hearing, meant to be held on Monday, was then postponed, according to World Watch Monitor.
The court has not given a reason as to why it was postponed and the case has been moved to a higher court.
The girl's lawyer has applied for bail.
A source told World Watch Monitor the girls had said they are "singing and praying here in prison."
Ethiopia ranks at number 18 on Open Door's World Watch List of the hardest places to be Christian.
The case will be heard on 14th October.
