Minister of Interior for Bavaria state Joachim Hermann announced the finding during a Nürnberg press conference.
"A video was found on the man's phone in which, according to a provisional translation, he threatens in Arabic to attack Germany in the name of Islam," Efe news quoted Hermann as saying.
He added that the suspect, in the same video, declared himself a follower of Abu Bakr al-Baghdadi, the leader of the Islamic State (IS) jihadist group.
According to Hermann, the man said he was seeking revenge against Germany because the country was getting in the way of Islam and had caused the death of Muslims.
"I think that after this video there is no doubt that the attack was a terrorist attack with an Islamist background," Hermann said.
Meanwhile, Federal Interior Minister Thomas de Maiziere said in a Berlin press conference that authorities did not rule out a terrorist motive, although he said it was also possible the attack was due to mental health issues.
The man who killed himself after detonating a homemade explosive device he carried in his backpack and left 15 injured, was a 27-year-old Syrian refugee who was set to be deported to Bulgaria after his asylum request had been denied, Efe news reported.
He had also made two suicide attempts and undergone psychiatric treatment, De Maiziere added.
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