The problem came to light after an endoscopy which stewards said detected a “degree of internal exercise induced pulmonary haemorrhage that may have affected the horse's racing performance”.
The gelding was given top weight of 59kg in the Doncaster, two kilograms more than he carried to win last year.
Happy Clapper's defection from the Doncaster leaves Goolphin stalwart Hartnell as topweight with 58kg.
“If you could guarantee me Happy Clapper would draw inside five then he'd be running in the Doncaster,” Webster said.
“But if he draws 20, with that weight, he can't win.
“I'd rather give him a nice easy trial on Friday and then we've got another two weeks to the Queen Elizabeth and hopefully he can run second to Winx again.”
The triple Group One winner has been placed six times in races Winx has won including his seconds at Group One level, among them the 2016 Doncaster.
Happy Clapper suffered a bleed from the nostrils in the Makybe Diva Stakes at Flemington in September and after the All-Star Mile, Webster was worried it had happened again.
“As trainers the first thing we look at when a horse doesn't run well is their noses but on the day I was happy to see he hadn't bled,” Webster said.
“It wasn't until later I found out about the internal bleed. It wasn't something I've experienced before.
“He seems fine. He's really bright and happy and has worked well back at Randwick.”