Astin posted a photo on his Facebook page of the actress holding him as a baby, along with a short tribute to his mother on behalf of his family.
Duke, whose real name was Anna Pearce, died this morning at age 69.
"This morning, our beloved wife, mother, grandmother, matriarch and the exquisite artist, humanitarian, and champion for mental health, Anna PATTY DUKE Pearce, closed her eyes, quieted her pain and ascended to a beautiful place," the family statement read. "We celebrate the infinite love and compassion she shared through her work and throughout her life."
"I love you mom," added Astin.
Other celebrities have also taken to social media to react to the news of Duke's death, including Rose McGowan, Claire Coffee and Willie Garson.
The Patty Duke Show was part of my evening lineup as a kid. Thank you for the inspiration and rest peacefully!— Claire Coffee (@clairecoffee) March 29, 2016
Rest with the Angels, Patty Duke. Thoughts and prayers are with all that love her.— Alyssa Milano (@Alyssa_Milano) March 29, 2016
Such a sad passing of Patty Duke, way too young, such a long career of impressive work and service. RIP— Willie Garson (@WillieGarson) March 29, 2016
Brave, outspoken & humanitarian who played Helen Keller in "Miracle Worker," Oscar winner Patty Duke passed. I will miss her. RIP.— Marlee Matlin (@MarleeMatlin) March 29, 2016