In a brief statement, Prince Harry and Meghan wished Catherine and her family "privately and in peace" healing.
Catherine said Friday the news was a "huge shock" after a "incredibly tough couple of months".
She reported feeling "well" and "getting stronger every day".
There has been no disclosure of the specifics of the cancer.
Kensington Palace claims the princess will recover fully.
In January, Catherine underwent abdominal surgery; however, at that time, it was not known whether or not she had any cancer.
Tests that were performed later confirmed that cancer had been present.
As of January 2020, Harry and Meghan have resigned from their positions as senior royals.