The body of Jeremy Richman, 49, was found in his Connecticut office building Monday morning, Newtown police said.
His death is the third suicide in the past week related to school massacres.
Police said they "will not disclose the method or any other details" of Richman's death, other than it does not appear to be suspicious.
"Our hearts are shattered, and our heads are struggling to comprehend" the foundation said.
The foundation described Richman as "a champion father," husband and neuroscientist who was on a mission to help "uncover the neurological underpinnings of violence" through the Avielle Foundation, which he started with his wife, Jennifer Hensel.
"Jeremy was deeply devoted to supporting research into brain abnormalities that are linked to abnormal behavior and to promoting brain health. Tragically, his death speaks to how insidious and formidable a challenge brain health can be and how critical it is for all of us to seek help for ourselves, our loved ones and anyone who we suspect may be in need," the foundation said.
"Jeremy's mission will be carried on by the many who love him, including many who share the heartache and trauma that he has suffered since December 14, 2012. We are crushed to pieces, but this important work will continue, because, as Jeremy would say, we have to."
The student has not been publicly identified. It's not clear under what circumstances the student died, or whether the apparent suicide was related to last year's massacre.
CNN's Julia Jones and Dakin Andone contributed to this report.