Police said the man had slashed four people at around 5 a.m at the station in the town of Grafing east of Munich.
A spokesman for the prosecutor's office later said one man had died from wounds suffered in the attack.
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Local media reported that witnesses had said the young man had yelled "Allahu akbar" ("God is greatest") during the attack.
The police spokesman said "a political background cannot be ruled out," adding that the man arrested was "not very cooperative".
Last August, two German-speaking jihadists claiming to belong to the Islamic State jihadist group threatened Germany with attacks in an online execution video, urging their "brothers and sisters" in Germany and Austria to commit attacks against "unbelievers" at home.
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