The Call Me By Your Name star, 34, who separated from Chambers in July 2020, began trending on Twitter last month and he later dropped out of an upcoming film with Jennifer Lopez.
Hammer had previously denied allegations arising following the leak, in a statement that appeared in The New York Times and Variety.
On Monday Chambers, 38, shared a message on Instagram in which she appeared to address the claims.
The TV personality said she supported “any victim of assault or abuse” and urged those who had suffered abuse to seek help.
Sharing an image of a beach, she wrote: “For weeks, I’ve been trying to process everything that has transpired. I am shocked, heartbroken, and devastated. Heartbreak aside, I am listening, and will continue to listen and educate myself on these delicate matters. I didn’t realize how much I didn’t know.
“I support any victim of assault or abuse and urge anyone who has experienced this pain to seek the help she or he needs to heal.
“At this time, I will not be commenting further on this matter. My sole focus and attention will continue to be on our children, on my work and on healing during this incredibly difficult time.
“Thank you for all of the love and support, and thank you in advance for your continued kindness, respect, and consideration for our children and me as we find ways to move forward.”
US actor Hammer played the Winklevoss twins in The Social Network and starred opposite Timothee Chalamet in acclaimed drama Call Me By Your Name.
Most recently he appeared opposite Lily James in a Netflix adaptation of Rebecca.
He and Chambers married in May 2010 and have two children.
Prior to their split, they had spent time self-isolating in the Cayman Islands amid the coronavirus pandemic.
Representatives for Hammer have been contacted for comment.