Police arrested Jose de Jesus Mendez Vargas, also known as "The Monkey", in the central city of Aguascalientes.
Mr Calderon described the capture as a great blow to organised crime.
La Familia has a reputation for gruesome violence but claims to protect local communities and promote family values.
Mexico's security spokesman Alejandro Poire said the arrest had "destroyed the chain of command" of the cartel.
The Mexican attorney general's office said Mr Mendez Vargas was "responsible for the transfer and sale of cocaine, marijuana, crystal methamphetamine in various states of Mexico and the US".
He is also accused of having masterminded the kidnappings and killings of rival gang members.
The government had offered a $2.5m reward for information leading to his capture.
A previous leader of La Familia, Nazario Moreno, was killed by security forces in December 2010.
His arrest led to a violent split in the gang. Mr Mendez Vargas is believed to remained head of the faction continuing under the name of La Familia.
The other faction, called the Knights Templar, is believed to be led by Servando "La Tuta" Gomez Martinez.
These gangs are active in parts of south-west and central Mexico, in particular Michoacan, the state of Mexico and Guanajuato, according to Samuel Gonzalez Ruiz, the former head of Mexico's organised crime unit.
For Mr Gonzalez Ruiz, Mr Mendez Vargas's arrest will not have a big effect on the ground.
"The impact will be totally limited because the illicit (drugs) market is there, the extortion is there, the kidnappings are there," he told the BBC.
In 2009, when La Familia was still run by Nazario Moreno, an assessment by the US Drug Enforcement Administration (DEA) said La Familia had a "Robin Hood-type mentality".
"They believe they are doing God's work, and pass out bibles and money to the poor. La Familia Michoacana also gives money to schools and local officials," the DEA said.
La Familia came to prominence in 2006 when suspected members threw five severed heads into a disco. A letter accompanying the heads declared: "Only those who deserve to die will die."
In December that year, President Calderon, who is from Michoacan, deployed troops to the state to take on the gang, later extending his drug fight to other parts of Mexico.
Since then at least 34,000 people have died, according to official figures.
The authorities have not updated these statistics since January.
Several top drug bosses have been arrested during the past four and a half years.
Police arrested Jose de Jesus Mendez Vargas, also known as "The Monkey", in the central city of Aguascalientes.
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