The group had to cancel six shows earlier this month (Aug14) when Parfitt was hospitalised in Pula, Croatia.
He returned to the U.K., where he subsequently underwent an operation to have a stent inserted to correct a problem with a graft that had become furred since it was inserted during his quadruple heart bypass in 1997.
Parfitt, 65, was due to rejoin the group and head back out on the road this week (ends15Aug14), however, he has been left with no choice but to sit out the next gig in Clumber Park in Worksop, England on Friday (15Aug14) after doctors ordered him to rest.
Freddie Edwards, son of bassist John 'Rhino' Edwards, will fill in for Parfitt for the one-off show - the first time he has missed a gig with the band since he joined in 1967.
Parfitt says, "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."
Quo co-founder Francis Rossi adds, "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 is expected to be fighting fit in time for the band's next scheduled concert at Holkham Hall in Norfolk, England on 23 August (14).