The 27-year-old man, a former soldier and member of the far-right GUD movement, is believed to have fired the fatal shot in Paris after an altercation in a café, while another far-right supporter who also fired on the ex-player remains on the run.
The killing occurred in the chic Saint-Germain district on the Left Bank of the French capital in the early hours of Saturday morning after Aramburu and friends became embroiled in an argument at a bar.
The row at the Mabillon café at around 6am on Saturday saw bouncers separate two groups, according to investigators.
After leaving the scene, two men are believed to have returned and fired several shots from a car at Aramburu, a 42-year-old former Argentina international, who died at the spot.
A 24-year-old woman arrested on Monday, believed to have driven the car, has already been charged as an accomplice to murder.
Aramburu played as a centre or wing, winning 22 Argentina caps including at the 2007 World Cup in France where he scored a try as the Pumas beat the hosts in the third-place playoff.
He played club rugby in France for Biarritz, Perpignan and Dax from 2004 to 2010, winning the Top 14 twice with Biarritz and later sitting on the club’s board of directors.
“There was an altercation, as there can be at the end of the evening. It was settled but the men came back and fired at Aramburu, who took three bullets,” a former Biarritz Olympique player who was with him told AFP on condition of anonymity.
Since his retirement from sport, Aramburu had lived in Biarritz and worked for a tourism company.
“This heinous crime and his death have left his family, friends and the world of rugby stunned and in unspeakable pain,” a lawyer for Aramburu’s family, Yann Le Bras, said in a statement on Sunday.