The 29-year old former Inter Milan and Deportivo Cali man succumbed to a problem that was bothering him for most of the 2012 campaign and had microfracture surgery in his left knee.
Rivas will be out for around five months and Impact head coach Jesse Marsch admits it is a massive blow for both the player and the first-year MLS club.
"In these situations, your thoughts are more with Nelson than the team in particular," Marsch told reporters.
"The initial signs and feedback is that the surgery went really well and that everybody's very optimistic about his recovery. We're all supporting him right now."