The 65-year-old musician had been due to return to the line-up tomorrow following a operation to correct a problem with his previous heart bypass.
But he has now been told to continue with his recuperation so a last-minute stand-in has been drafted in for a single show.
Freddie Edwards - son of bass player John "Rhino" Edwards - will step in for the concert at Clumber Park in Worksop, Nottinghamshire.
Parfitt fell ill during the band's European tour and was flown home from Croatia to be treated at the Royal Brompton Hospital in London. He had a stent inserted after it was found a graft from his 1997 quadruple heart bypass had become furred.
Parfitt said: "Obviously I'm really disappointed to be missing this show but I'm pleased that Freddie will be able to step up and help the band out whilst I'm recuperating.
"I know all the Quo fans will make him welcome and I'll be back onstage soon."
His fellow guitarist and long-time sidekick Francis Rossi said: "It will certainly be strange performing without Rick, but Freddie performed with me when I did my solo tour so I know that he's got what it takes - and, of course, he's part of the Quo family."
Parfitt has weathered drink, drug and health problems over the years but the band has never gone ahead with a show without him since his arrival in the line-up.
John Edwards said of his son's opportunity: "This is going to be an amazing experience for us - what a day for the family."
Parfitt has been cleared to return to the band by the time of their next show at Holkham Hall in Norfolk on August 23.
Quo manager Simon Porter said: "Our priority is, of course, to do everything we can to get Rick back onstage as soon as possible, but we hate letting down the fans and we're delighted that this show will still go ahead.
"Rick is making a fantastic recovery, but his doctors have yesterday advised just a few more days' recuperation before hitting the stage again for a full-voltage Quo show.
"This is a real piece of Quo history in the making. Rick will be back soon but, in the meantime, we look forward to welcoming Freddie into the fold for what we are sure will be a memorable one-off."