Kaley Cuocu © A Kovacs/Wikipedia
Cuoco, who lives in San Fernando Valley, California, was hospitalised with the injury.
Filming of this week's show will be without the star, with the script hastily adjusted to write her out.
There are plans to write future scripts around her absence if she is unable to return to work in the short term.
The show was to take a scheduled production break next week. It is not yet clear when Cuoco will be able to return.
Cuoco, 25, keeps horses on her San Fernando Valley farm, and only recently told TV Guide magazine in the United States of her love for horses.
"That's my secret life," she told the magazine. "I've been completely into that since I was 16."
She said her horse, named Falcon, was the man in her life at the moment.