The Atomic Blonde star posted a photograph of her and August having a nap on their sofa with one of their dogs on Tuesday.
In the picture, the 46-year-old actor is asleep with one arm around her daughter, who is wearing a hi-tech eye mask over her face to help her snooze.
Both mother and daughter are cosied under a colourful Care Bears blanket, while a fluffy white dog lays beside Theron.
Theron wrote in the caption: “New year, same energy. C’mon 2022, don’t be a b****!”
Comedian Chelsea Handler wrote in a comment: “Nice eye shades, Auggie!” while Lindsay Lohan said: “Wow love this so much.”
Also referring to the eye mask, January Jones of Mad Men fame added: “Omg I got Xander that eye mask massager thing for Xmas.”
Theron is also mother to nine-year-old daughter Jackson, who is transgender. Both children are adopted, with Jackson hailing from South Africa and August from the US.
The Mad Max star prefers to keep her family out of the public eye, but she has previously shared a video and pictures of her and her daughters spending time together on social media.
In August, she posted a slow-motion video of the three of them holding hands and jumping off a yacht into the sea during a summer holiday.
Theron also posted a tribute to her daughters in September 2020 in honour of National Daughters Day. Alongside a collection of images, she wrote: “My heart belongs to these two beautiful powerhouses. I will never be the same. Happy #NationalDaughtersDay.”
In 2019, Theron opened up about when she discovered Jackson, who was born male, identified as a girl when she was three years old.
In an interview with the Daily Mail, she said: “Yes, I thought she was a boy too. Until she looked at me when she was three years old and said: ‘I am not a boy!’
“So there you go! I have two beautiful daughters who, just like any parent, I want to protect and I want to see thrive.
“They were born who they are and exactly where in the world both of them get to find themselves as they grow up, and who they want to be, is not for me to decide,” Theron added.
She said her job as a parent is to “celebrate them and to love them and to make sure that they have everything they need in order to be what they want to be”, adding she would do “anything in my power for my kids to have that right”.