Kate, 32, was scheduled to attend the opening of the Clore Art Room at London's Barlby Primary School as part of the Clore Duffield Foundation's 50th anniversary year.
However, Kate, who has been a Royal Patron of the Art Room since 2012, was forced to cancel due to the ongoing effects of hyperemesis gravidarum, a severe pregnancy sickness she also suffered when carrying George, who is now 14 months old.
The symptoms – intense nausea and vomiting – are "similar in severity to last time," a royal source confirms to PEOPLE.
But it is unknown as to when Kate will actually "turn the corner" and feel well enough to continue with her public duties, a royal source says.
Meanwhile, adds the source, the Duchess "continues to be unwell and we are keeping things under review."
"I am truly sorry that I cannot be with you all today as you celebrate this milestone," Kate said in a statement. "My sincere apologies for not being able to join you, but I hope that I will have an opportunity to visit Barlby and see the Clore Art Room soon."
The palace would not say if other engagements had been canceled.
"As with all her engagements, we are taking decisions closer to the time of them occurring, and we are keeping them under review," a palace spokeswoman says, adding that this one was made public due to the fact that the engagement still took place and that Kate was "really keen to send her support because she couldn't be there in person."
She is thought to be at home at Kensington Palace.
Reporting by SIMON PERRY