Ms Gordillo, 68, is known simply as "la maestra" or "the teacher"
No-one from her legal team has responded to the allegations, but in the past she has denied any wrongdoing.
Her arrest came a day after the government enacted major reforms to the education system.
President Enrique Pena Nieto signed the sweeping reforms, which seek to change a system dominated by Ms Gordillo's union in which teaching positions could be sold or inherited.
Controversial union chief
- Elba Esther Gordillo rose from humble origins in rural Chiapas state
- Leads the SNTE teachers' union, with an estimated 1.5 million members
- Has held post for more than 20 years
- Prosecutors have never brought a charge against her despite numerous fraud allegations
- Expelled from President Pena Nieto's Institutional Revolutionary Party in 2006 for forming her own party
- Accused by prosecutors in February 2013 of "systematic embezzlement" of union accounts between 2008 and 2012
"We are looking at a case in
which the funds of education workers have been illegally misused, for
the benefit of several people, among them Elba Esther Gordillo,"
Attorney General Jesus Murillo Karam said.
His office alleges Ms Gordillo, 68, used the money on property, including in the US, private planes and plastic surgery. The BBC's Will Grant in Mexico City says that Ms Gordillo is one of the highest profile figures in Mexican political life, known simply as "la maestra" or "the teacher".
For more than 20 years she has led the National Union of Education Workers (SNTE).
Attorney General Jesus Murillo gives details of the arrest
Ms Gordillo has held real influence over governments and individual presidents by persuading her union members to vote as a single bloc, our correspondent says.
The teachers were also responsible for manning polling stations on election day.
Her union is very wealthy, and can count on an annual budget of tens of millions of dollars.
It is on claims that she mishandled those funds, allegedly diverting money intended for the union's coffers to her personal accounts, that she has now been arrested.
The education reforms appeared set to weaken the SNTE, which has largely controlled access to the profession.
The union has argued that reforms could lead to massive lay-offs.
Critics also say the changes could signal the start of the privatisation of education in Mexico.
Mexico's education system currently ranks bottom in a list of members of the Organisation for Economic Co-operation and Development (OECD).
The reforms will require teachers to undergo regular assessments, something that has previously never taken place inside Mexico's primary and secondary schools.
Many teachers in Mexico are said to have a very low standard of education themselves.
Another change is intended to tackle the problem of absent or even deceased teachers receiving wages.
Ms Gordillo has been an outspoken critic of the current education minister and his approach to the reforms.
Source:BBC