Daly initially said he would try to play “through the pain” of degenerative arthritis in his right knee after seeing his request to use a golf cart turned down by the R&A on Saturday.
However, the 53-year-old has since had a change of heart and has been replaced in the field by American Kevin Streelman, with Rory Sabbatini now first reserve for the final major of the year ahead of Brian Harman and Martin Kaymer.
Daly had been allowed to use a cart in the US PGA Championship in May under the Americans With Disabilities Act, although he missed the cut at Bethpage.
But although the R&A expressed sympathy with Daly over his condition, it said players “walking the course is an integral part of the Championship and is central to the tradition of links golf which is synonymous with The Open”.
After receiving the news, Daly wrote on Twitter: “Quite disappointed they do not see it the same way our PGA of America and PGA Tour sees it. Different continents different laws???
“As a proud Open champion, I know what the Open Championship represents and what a special tournament it is.
“All who have earned the right to compete should be afforded that right to compete and give it their best shot.
“While I trust the R&A’s decision was made with good intentions, I could not disagree more with their conclusions.”
Daly said he had been advised his doctor he would need “either unicompartment or total knee replacement”.
He added: “Before that comes my plan is to give it a shot in 2 weeks at Portrush. Fingers crossed I can make it thru the pain.”