"The judge ordered the arrest of Don Luis on the charge of genocide ... and ordered his house arrest," his lawyer, Juan Velazquez, said, adding the former president was "at home and will remain there.”
The arrest order came as a surprise as Mexicans readied for this weekend’s presidential elections and came one year after a federal judge dropped charges against the 84-year-old in connection with a similar case in 1971, in which security forces killed at least 12 people.
Mr Echeverria was president from 1970 to 1976 during Mexico’s “Dirty War” against opponents of the ruling Institutional Revolutionary Party.
He was interior minister in 1968, when he allegedly ordered security forces to use force to crush anti-government protests shortly before the opening of the summer Olympic Games in Mexico
City.
The event, which came to be known as the Tlatelolco massacre, allegedly resulted in the killing of up to several hundred students, but the death toll was never made public.
Mr Echeverria has denied any responsibility in the 1968 and the 1971 killings.
"We will demonstrate that like the events in 1971, those of 1968 did not constitute a genocide. They were most unfortunate deaths, but in no way were they part of a systematic persecution by the state," his lawyer said.
Investigations into the events were only launched after Vicente Fox, of the National Action Party, won the 2000 presidential election, ending 71 years of authoritarian rule by PRI.
When he took office, Fox pledged to investigate and punish anyone responsible for human rights violations, but only a few mid-ranking officials had been arrested to date.
The PRI's candidate Roberto Madrazo is ranked third in opinion polls ahead of Sunday's presidential election, seen as a tight race between leftist Andres Manuel Lopez Obrador and conservative Felipe Calderon of the ruling National Action Party.