The chopper was on a reconnaissance flight eight kilometers east of the state capital of Ciudad Victoria near the US border when it came down, the defense ministry said in a statement.
The cause was unknown, media reported.
The aircraft was carrying two pilots and an army officer. The co-pilot, the sole survivor, was airlifted to hospital.
Tamaulipas is one of Mexico's most violent states, where the Zetas and Gulf cartels are fighting for control of key drug-trafficking routes to the United States.
In September five crew died in a police helicopter accident in the state of Michoacan. Experts said the incident took place when the pilot was allegedly conducting evasive maneuvers to avoid fire from a criminal gang.
That was the second time since 2015 that a gang had downed a helicopter. Last year the Jalisco New Generation drug cartel in the western state of Jalisco used a rocket launcher to hit a military helicopter, killing seven soldiers and a policewoman.
In July this year three soldiers died in another military helicopter accident in central Mexico.
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