Reports say the five men who raped the young woman recorded the act, which was later uploaded to the Internet.
The incident, which is believed to have occured in Abia State sparked outrage nationwide.
He, however, expressed doubts that the suspects would be convicted based on the available evidence.
Abdullahi said this in Lagos at a meeting with youth organisations.
The minister said, "More than 70 per cent of the information we have on the rape will not be said here for obvious security reasons. But I can tell you we have information on it.
"The girl is not a student of Abia State University. She was raped in an off-campus residential area of students.
"One of them (suspects) has been identified conclusively."
Although the faces of the rapists are not seen in the video, the minister said the National Human Rights Commission was on top of the situation.
He said, "Some legal experts have told us that it may be difficult to convict the rapists because the video does not reveal the face of the victims.
"The National Human Rights Commission is working with the Ministry of Youth Development. The commission, which is headed by a competent lawyer, is on top of this case.
"This is law, if we can not press for rape, there are other charges that we can press. I can assure you that justice will be done."
The minister, at the meeting, fielded questions from some of the 50 selected participants, among whom were Fela Durotoye and Omotola Jolade-Ekeinde, on national issues bearing on youth.
He promised that his ministry would organise a conference for not just potential rape victims but potential rapists, to address the ugly trend among youths.