The statement said there had been an arrest warrant for Carlos Beltran Leyva since 2008.
Carlos Leyva is one of five brothers who allegedly ran the Beltran Leyva Cartel, one of Mexico's most powerful drug organisations notorious for their grisly killings.
His brother Arturo, the reputed head of the cartel, was killed in a shootout with Mexican marines in the central city of Cuernavaca on December 16.
Days after the incident, armed men massacred the mother and three relatives of a soldier who was killed in that shootout.
Mexican officials in the past have described Carlos Beltran as a key member of the gang, but it was unclear if he took over as chief of the cartel after his brother died.
A third brother, Alfredo Beltran Levya, was arrested in January 2008.
Another brother, Mario Beltran Leyva, is still at large and listed as one of Mexico's most wanted alleged drug lords.
The Reuters news agency reported a security ministry source as saying that Beltran Leyva had been transported to Mexico City.
The Beltran Leyva brothers worked side by side with Joaquin "El Chapo" Guzman, the leader of the Sinaloa Cartel.
They reportedly broke away after Osiel Cardenas, the head of the Gulf Cartel, was arrested in 2003 and quickly seized the lucrative drug routes in northeastern Mexico.
The arrests have also raised concerns of a possible turf war over the areas the cartel controls.
A possible indication of that came on Wednesday, when the bound and beaten bodies of two men were found hanging by their necks from a highway overpass in the Sinaloa town of Los Mochis.
A message on a piece of cardboard found nearby and thought to be from the Beltran Leyva cartel said in part: "this territory already has an owner".
Despite the government's deployment of 49,000 troops across Mexico in its war on drugs, broad daylight shootings are common and killings by drug gangs soar to an unprecedented 7,000 last year alone.