Lam uploaded a selfie to social media hours after she was discharged from hospital, explaining how she fell in Government House on Monday night.
She said she slipped on the stairs before a farewell dinner at her official residence for retiring colleagues, and at first she thought she just had some scratches.
But Lam said she decided to go to hospital after the pain grew. She said an X-ray at Queen Mary Hospital showed part of her right elbow was chipped and a cast was needed to help it recover.
“The biggest problem now, I’m afraid, is putting on clothes and writing!” she said.
The chief executive said she will take the opportunity to get some rest, pointing out that she hadn’t taken leave for nearly three years.
Lam said she will be back leading Hong Kong once again after “recharging”.
Chief Secretary John Lee will be acting chief executive in her absence.