According to reports, the former Argentina international was shot dead in France on Saturday.
According to L'Equipe, Aramburu was killed in a drive-by shooting in Paris.
According to the French newspaper, he was involved in an argument in a bar with a group of people who later returned in a car and shot him.
The suspects in a murder investigation have not yet been found, according to the Paris prosecutor.
Before joining Glasgow Warriors in 2010, he had spent time at French clubs Perpignan, Biarritz and Dax.
The Warriors said they were "shocked and saddened" by Aramburu's "sudden and tragic death".
The thoughts of everyone past and present at the club are with his family at this difficult time.
The Pumas said they "will not forget his tries and his performance" at the 2007 World Cup, where he scored two tries.
Biarritz sent its most sincere sympathies to his family and assured them of its total support.