In the snapshot, the 41-year-old actress appears holding Booker as he sleeps, she captioned the image "Happy Holidays."
Booker is the third child for Newton and husband Ol Parker. He was born March 3.
"Our baby boy is finally here! Booker Jombe Parker. Born joyously at home yesterday," Newton tweeted the day after she welcomed him in a home birth.
Newton and Parker have been married since 1998. The couple welcomed their first child, a daughter named Ripley, in 2000. The pair's second child, a son named Nico, was born in 2004.