Kate, who is expecting her second baby with husband Prince William, had been due to carry out a visit for the charity The Art Room in Oxford yesterday (1 October).
The pregnant Duchess had been hoping to open the charity's ninth centre in Ladbrook Grove, London, but was forced to cancel. She did, however, send a letter of apology.
In the heartfelt note, Kate said: "I wanted to share my congratulations with you all for the launch of the new Clore Art Room. I was looking forward to joining you all for this particularly special day as part of the Clore Duffield Foundation's 50th anniversary year.
"I am truly sorry that I cannot be with you all today as you celebrate this milestone. As patron of The Art Room, I feel great pride to see the work that the charity is doing.
"Vulnerable children flourish in the safe havens that The Art Room provides; this highlights just how important it is to support children at a time when they most need help and support."
Last month, it was confirmed that Kate and William - who are already parents to son George - are expecting their second child together.
However, the news was announced early as Kate has been suffering from hyperemesis gravidarum again. When she was pregnant with George, Kate was hospitalised for the condition, however this time she has been receiving treatment at Kensington Palace.
Following the baby news, Kate pulled out of the Invictus Games opening ceremony and a scheduled visit to Malta.
Officials have again confirmed that future decisions over royal visits will be made "on a case-by-case basis".
Speaking about Kate's absence at the Art Room function yesterday, a Palace spokesman said: "The Duchess of Cambridge continues to suffer from the effects of hyperemesis gravidarum and was unable to attend this event in person.
"The decision to undertake engagements is being kept under review on a case-by-case basis."
Kate Middleton's second pregnancy: Celebrities send their congratulations