Ms Gordillo, who runs the 1.5 million-member Mexican teachers’ union, is alleged to have diverted about $200m from union funds to personal accounts.
No-one from her legal team has responded to the allegations, but in the past she has denied any wrongdoing in handling the funds.
The arrest came after major reforms to the education system on Monday.
President Enrique Pena Nieto signed the sweeping reforms, which seek to change a system dominated by Ms Gordillo in which teaching positions could be sold or inherited.
“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, spent the funds on plastic surgery and a luxury home.
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).
With an estimated 1.5 million members, 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 reforms appeared set to weaken the powerful teachers’ union, 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, with some only having graduated from high school.
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.