Tomas Zeron, who previously led Mexico's Criminal Investigation Agency, is accused of manipulating the probe into one of the country's worst human rights tragedies.
Zeron is one of the architects of the so-called "historical truth," the official version of the case presented in 2015 that was rejected by the victims' relatives and independent experts.
"Israel is protecting Tomas Zeron, a human rights violator who tortured those he detained at the time to build the 'historical truth,'" Meliton Ortega, a representative of the students' families, said.
Hundreds of protesters gathered outside Israel's embassy in Mexico City, with no visible police presence.
Some carried pictures of the missing students while others sprayed graffiti on the embassy walls.
Mexico has repeatedly asked Israel to hand over Zeron, who is accused of kidnapping, torturing suspects and manipulating evidence -- allegations he has denied.
The 43 teaching students had commandeered buses in the southern state of Guerrero to travel to a demonstration in Mexico City before they went missing.
Investigators say they were detained by corrupt police and handed over to a drug cartel that mistook them for members of a rival gang, but exactly what happened to them is disputed.
So far, the remains of only three victims have been identified.
Last month, a truth commission tasked by the current government to investigate the atrocity branded the case a "state crime" involving agents of various institutions.
It said that military personnel bore "clear responsibility," either directly or through negligence.
Prosecutors announced last month that arrest warrants had been issued for more than 80 suspects, including 20 military personnel, 44 police officers and 14 cartel members.
The same day, former attorney general Jesus Murillo Karam, who led the controversial "historical truth" investigation, was detained on charges of forced disappearance, torture and obstruction of justice.
Last week, the government said that an army general and two other military personnel had also been arrested.