Cooper, 84, died May 8 after having played Katherine for nearly 40 years.
"Y&R" Executive Producer Jill Farren Phelps told TV Guide episodes of the show have been taped for airing into the summer but Cooper's character will ultimately die on the series.
"We've already written the show into July, so it will take some time before we can address her departure on air," Phelps said.
"In the meantime, there will be references in the script that Katherine and her husband Murphy are off somewhere on a trip."
Phelps went on to say she decided it is important for the audience, as well as the show's characters, to have closure regarding Katherine.
"Contrary to rumors, we never gave a thought to recasting the role -- not for a minute! 'Y&R' was forced to do it when Jeanne was out ill for a bit a couple of years ago, when she was replaced by Michael Learned. But that was a temporary situation. You cannot replace the irreplaceable. The greatest way to honor Jeanne is to make Kay's exit as dramatic and meaningful as possible," Phelps said.