The fight took place in the city of Kaunas, about 75 km northwest of the Lithuanian capital of Vilnius or 60 km east of the border with the Russian exclave of Kaliningrad.
"At about 2 am on June 15 in Kaunus's Laisves Alley, a conflict broke out between two drunken citizens of Azerbaijan and a US servicemen, in which the American soldier was injured," a statement released by the press service of the Kaunas district police commissariat said.
One of the Azerbaijanis has been arrested, with the details of the incident being investigated.
On Friday, NATO and its partner nations wrapped up the Saber Strike drills, which saw several incidents across the three Baltic countries since they began on June 3. Last week, the Lithuanian Defense Ministry reported that at least 13 US servicemen were hurt after four Stryker armored personnel carriers got in an accident while moving in a convoy. Two days later, another Stryker drove off the road and crashed into a tree in the city of Kazlu Ruda. Earlier this week, a light vehicle with two NATO troops inside rolled over, injuring its occupants.