Juan Gerardo Treviño, also known as "El Huevo" or "The Egg," was captured at dawn on Monday by Mexican authorities.
A violent gun fight between the military and gang members ensued in Nuevo Laredo, a city on the Mexico-US border.
A US citizen and on a "wanted" list, he is facing drug trafficking and money laundering charges there.
He is also accused of murder, terrorism, extortion and criminal association in Mexico, the government told Reuters news agency.
The capture of the high-profile cartel leader is "one of the most important arrests of the last decade", Mexican Secretary for Foreign Affairs, Marcelo Ebrard told CB Televisión.
Juan Treviño was arrested in the state of Tamaulipas, one of Mexico's most violent regions. A few days earlier, local authorities had announced a $100,000 reward for his capture.
He is accused of leading a powerful criminal organisation, the Northeast Cartel, and its armed gang, Troops from Hell.
Mr Treviño's family is also connected with organised crime groups in Mexico. His uncle is Miguel Ángel Treviño Morales, once the leader of the infamous drug cartel Los Zetas. Now serving a life sentence, he was accused of ordering massacres and running drugs on a global scale.
Los Zetas members became particularly infamous for their brutality, often torturing and decapitating their victims. The gang is now largely disbanded and has splintered into several groups, including the Northeast Cartel.
Juan Treviño's arrest caused a retaliatory gun fight by members of his cartel in the border city of Nuevo Laredo, which is situated opposite Laredo in Texas. Some 700 military troops and four helicopters were needed to secure the area.
Videos shared on social media showed large lorries on fire and roads blocked. Several international bridges between the US and Mexico were closed due to the unrest.
Mexico's secretary of national defence said that 38 government facilities and 22 military headquarters were attacked. The US consulate in the city also confirmed it was damaged and was forced to close temporarily.
The state of Tamaulipas is known for violent killings and disappearances, often linked to powerful drug cartels who battle for territory.
Many migrants also try to cross the border into Texas from there.