The Crystal Palace chairman and former Tag Worldwide chief executive was revealed as one of two new dragons last week.
He was set to replace Moonpig’s Nick Jenkins.
However, Parish has subsequently decided that the potential commitment would be too much, according to a BBC media announcement: “On reflection, I have come to the conclusion that I couldn’t give Dragons’ Den the time and commitment the show needs and that the entrepreneurs deserve, therefore I have decided to give up my Dragons’ seat to someone else,” he said.
Parish will be replaced by Tej Lalvani, the chief executive of the Vitabiotics vitamins and supplements business.
A number of Crystal Palace fans immediately took to Twitter to suggest that Parish should spend his now-going-spare Dragons' Den funds on centre-back Mamadou Sakho, currently on loan from Liverpool.