The first quake, of 4.6 magnitude, struck in the early hours just south-west of the town of San Juan.
The National Institute for Earthquake Prevention says the epicentre was at a depth of 117 kilometres, while the US Geological Survey (USGS) registered the depth at 96 kilometres.
The second tremor, a stronger 5.3 magnitude quake, occurred 660 kilometres to the north, in uninhabited woodland near the village of Juan Bautista Alberdi, along the same Andes range.
The later quake was at a depth of 28 kilometres, according to the USGS.
The quakes were among several to hit South America and the Caribbean in recent days, and came one week after a massive 7.0 magnitude earthquake hit Haiti, levelling the capital city of Port-au-Prince.
The Haitian Government says number of confirmed deaths from the Haiti quake has risen to 75,000, while 250,000 were injured and 1 million left homeless.
The town of San Juan has been hit several times in the past, the worst being in 1944 when 8,000 people were killed by a 7.4 magnitude upheaval.