In a statement to the Sun on Sunday, the couple, who share a one-year-old son, said it was "with great sadness that we have decided to have some time apart".
The couple’s statement added: "We both remain completely committed to raising our beautiful boy Billy together.
"We ask that you respect our privacy during this difficult time. Thank you."
Ms Smith is known for her roles in dramas such as Mrs Biggs and Cilla and for her work on stage in Legally Blonde and Funny Girl.
She gave birth to their son Billy in May 2020 amid the coronavirus pandemic.
The couple’s split comes a week after Ms Smith celebrated her 40th birthday, sharing a picture with her son as she thanked fans for their well-wishes.
She wrote alongside a photo of them standing by a stunning balloon display with the number ’40’ adorned in gold: ‘Thank you all so so much for your beautiful birthday messages! Means the world Xx #40yearsyoung’.