The minister made the remarks at a media briefing at the Secretariat on Wednesday after police pressed charges against 25 suspects over the murder of the BUET student.
Abrar, a second-year student of electrical and electronic engineering, was bludgeoned to death by leaders and activists of BCL in his dormitory on Oct 6 after he criticised the government over a water-sharing deal with India on Facebook.
The call for a speedy trial was one of several demands placed by angry students during the heated protests on the BUET after the incident.
The Detective Branch of Police filed charges against 25 suspects in the case within five weeks of the incident on Wednesday.
"The home ministry has to apply for a speedy trial. Once that is done, the legal process to hold the hearing at a speedy trial tribunal will be initiated and the trial proceedings will be completed swiftly," said Anisul.
According to the minister, the case will be disposed of in 135 days at most if it is tried by the speedy trial tribunal.