The judge gave the order when responding to a petition for Kabuga to be temporarily transferred to The Hague given the current travel restrictions.
The 84-year-old Kabuga, who was arrested on May 16 near Paris, had been on the run for 25 years. He is accused of financing the 1994 genocide which left about one million people dead.
The tribunal wrapped up five years ago and its responsibilities were transferred to the Mechanism for International Criminal Tribunals (MICT), based in The Hague. The MICT also has an office in Arusha.
“Any variation to this mandate should be exceptional,” Judge William Sekule of the MICT Arusha branch said.
“If transfer to the Arusha branch is not possible at the relevant time, appropriate relief may be sought,” Sekule added.
According to a prosecutor, Serge Brammertz, international war crimes investigators had requested that Kabuga, the alleged financier of the 1994 genocide, be transferred to United Nations custody for trial.
Kabuga was first arraigned in a court in the French capital, Paris, on May 20 where he said he wanted to be tried in France.
His lawyer said that Kabuga believed he would not receive a fair trial in an international court as it was politically biased and he was to week to be transferred.
The court is expected to rule on June 3 whether to hand Kabuga over to the MICT, whose arrest warrant states that he be transferred to Arusha.
Kabuga had been indicted in 1997 on seven criminal counts, including genocide, incitement to genocide and crimes against humanity, and had a $5 million reward for his capture.