Rojo, 29, has joined on a six-month loan deal, according to local press.
He has 18 months left on his contract with the Premier League side but has fallen down the pecking order at Old Trafford since a bright start to his career in England. Having made 59 Premier League appearances during his first three seasons at United, Rojo has played in just 17 league encounters in the last two-and-a-half years.
Rojo, who can play at centre-back or left-back, hasn't played for the Red Devils since November when he picked up an injury.
He was left out of Argentina's 2019 Copa América squad in June but played in two friendlies in September and October. He was picked for two more friendlies in November but had to pull out of the squad through injury.
It's believed his move back to Estudiantes is to gain vital game time ahead of the next Copa América starting in June, which is co-hosted by Argentina.
Rojo has played 61 times for Argentina and was part of their 2014 and 2018 World Cup squads.