The star, best known for her role as broody Jane Beale in the BBC soap, is due to give birth in early summer.
Brett's pregnancy will be hidden on screen as Jane is unable to have children following a hysterectomy.
A source told the News of the World: "Laurie's over the moon. Many of her plotlines centre on Jane's desire for kids. But after she was shot in the stomach by hubby Ian's stepson Steven that won't happen naturally."
The insider added: "It's going to be tricky for producers to hide Laurie's bump. We'll no doubt see her hiding behind carefully placed piles of cakes and sandwiches in the café for the next few months!"
Brett is thought to have been in a relationship with her current partner since 2009.