“There was no violence in the operation,” a spokesman said on Tuesday, adding that the mayor and his wife had been taken to federal prosecutors to be interrogated.
Two security officials said Abarca and his wife were detained without resisting, the officials spoke on condition of anonymity because they were not authorised to speak to the press and provided no other details.
The couple are in the custody of the Attorney General’s Office, where they were giving statements.
The arrests come more than a month since the students vanished after they were attacked by municipal police linked to the Guerreros Unidos drug gang in Iguala, 200km south of Mexico City.
Al Jazeera’s Rachel Levin, reporting from Ayutla in Guerrero State, said: “Parents have been extremely frustrated with this investigation, they repeatedly say how is it possible that when you have the federal police and the military involved they are still not able to find these 43 missing students.”
One of the lawyers representing the famiies of the disappeared told Levin he believed the arrests could be a huge breakthrough in the case.
Levin said: “The families have also insisted that the mayor and his wife were responsible for the disappearance of the students.
“Floriberto Cruz Evangelista said he hopes that with these arrests he will find out what happened to his son.”
Abarca, his wife, and the city’s police chief went on the run two days after the September 26 police attack.
Authorities say Abarca ordered the officers to confront the students over fears that they would derail a speech by his wife, who was the head of the town’s child protection agency.
The mayor and his wife have since been linked to the Guerreros Unidos gang. Pineda also has three brothers who are known members of the Beltran Leyva drug cartel.
Abarca’s family says he is innocent. The government is still searching for the students.