Speaking on ITV's Loose Women, Sawalha, 51, said she and husband Mark Adderley have only just realised their open conversations about the news have been slowly causing problems for Kiki.
Sawalha said: "Today, and this does make me sad, I’m taking Kiki for her first appointment to see somebody for anxiety.
"[My husband and I] talk a lot about the news, we have the newspapers all the time, and she has taken so much of it in. Her anxiety is about safety.
"We are really guilty of oversharing, and have only just realised that's causing real problems."
Jeremy Todd, chief executive of Family Lives said Sawalha shouldn't feel guilty about discussing current affairs with her children, although she may need to be careful about how she broaches the subject.
"Any communication with children needs to be based upon the ability to understand what is being spoken about," Todd said when speaking to HuffPost UK Parents.
"We wouldn't say the broader idea of talking about current affairs is the wrong thing to do.
"Parents just need to understand the capabilities of their children before they discuss. It's more about understanding the triggers that cause distress and upset.
"Equally, it's probably quite a dangerous thing to remove conversation completely that is controversial."
A spokesperson from the NSPCC said it's "crucial" that parents reassure and comfort their children, who will be relying on them for stability in troubling times.
Todd agreed with the NSPCC and said parents also have a responsibility to recognise danger and complicated events, and know how to communicate this to their children.
"To remove and sanitise things makes the child more vulnerable and more shockable," Todd added.
Todd said taking into account a child's age is important when choosing to discuss such topics, but however young the child parents shouldn't avoid certain topics as the easy accessibility of the internet means many children will be exposed to topical news stories whatever their age.
"It's about finding a sensible approach to the information that's available, that takes into account their age," he explained. "The right approach will help children find a better way to cope, than avoiding the topic completely."
Amanda Gummer, child psychologist and founder of Fundamentally Children agreed your child's age will affect the way you approach the topic.
"If children are old enough to ask the question, they're old enough to have a conversation," she told HuffPost UK Parents.
"If they're not interested, don't force it on them - don't scare them if they don't have the context of what's going on.
"A two-year-old might ask questions about something in the news but won't necessarily process the information as an eight-year-old would.
"You wouldn't need to go into much detail for the younger children because they don't put any more significance on that than they do other things in every day lives."
Todd also raised the point that children are more likely to get anxious if they feel their parents aren't telling them the truth or covering something up.
"This can cause huge anxiety," he added. "There's no point not acknowledging things that are in the news.
"Talk about it as a family and talk about things you're doing to make sure you're sensible in that situation.
"You can't just remove the idea that life is challenging and outright unfair, that's not helpful."