Konstandopoulos ruptured his left ACL at training on Monday, a year after suffering the same injury to his right knee.
He is due to undergo surgery on Tuesday.
"After working hard, coming back and scoring goals it pains me to say that after one year I have ruptured my other ACL," Konstandopoulos said on Instagram.
"I know the process, I know the grind, I know that I will be back stronger again.
"Nobody works as hard as me and I will prove it again. See you again in 9 months better than ever."
The 24-year-old returned for the start of the 2020-21 season and scored two goals in seven appearances for Carl Veart's eighth-placed Reds.
"This is extremely unfortunate news for Nathan and we're all feeling for him at this time," Adelaide football director Bruce Djite said.
"We saw how determined Nathan is as a person to return from such a major setback, and we have complete confidence in him that he will return from this one.
"Adelaide United is completely behind Nathan and we will continue to support him during his recovery and return to football."