The Argentine centre has been told the injury will prevent him from playing rugby for six months.
Glasgow Warriors, who signed Ascarate on a one-year deal last summer, have now allowed the 25-year-old to recuperate in Argentina.
Glasgow Warriors head coach Gregor Townsend said: “We’re really disappointed for Gabriel that he’s had to leave the club early. He fitted in really well and would have played a big role in the second half of the season.
“Although he will not require surgery, he has been advised not to take any contact for six months, so we agreed to release him from his contract early to allow him to return home.
“We’d like to thank Gabriel for his contribution to the club during his time here and we wish him well for the future.”