Davies added: “This is the last thing I want, but there’s no other way. I fear if I keep ‘pushing through’ I will be battling with this for longer than I need to be.”
There are no details about how long she will be out of action for. The tour began in Leicester last month and has 10 months left to run.
The 29-year-old said she “can’t wait to be back on stage and feel like me again”.
Davies rose to fame when she won Love Island in 2017, and has had roles in musicals including in Pretty Woman and 9 to 5.
She starred in The Great Gatsby last year – a performance that earned her a WhatsOnStage Award at the weekend – and then joined the last series of Strictly Come Dancing in September as a late replacement for Dani Dyer.
Davies made it all the way to the Strictly final in December before beginning rehearsals for Legally Blonde.
“I keep having to remind myself I went from Gatsby, to a last (minute) Strictly, then to Elle so my body’s evidently fighting for its life,” she wrote, along with laughter and hand heart emojis.
“I also keep reminding myself that it’s OK to be poorly, we are human.
“Just a reminder there’s absolutely never a right time to be poorly in a musical theatre schedule so you must, for your own sanity, go with the flow.”