The rocker was flown home from Croatia this week and treated at the Royal Brompton Hospital in London where he had a stent inserted after it was found a graft inserted during his 1997 quadruple heart bypass had become furred.
The band's manager Simon Porter said: "We are all obviously delighted that Rick has made such rapid progress, especially as the band is shortly to unveil another exciting and innovative new project, details of which will be announced in the next couple of weeks."
They shelved six shows after Parfitt was taken ill but Mr Porter said planned shows in Nottinghamshire and Norfolk later this month would go ahead as planned.
Parfitt had a quadruple heart bypass after doctors said he could die at any time following a hard-living lifestyle involving drink and drugs.
Even after the life-saving surgery, the guitarist said he would not become a ''born-again Christian'' and still enjoyed the ''odd pint''.
Nine years ago Parfitt - who leads Status Quo with Francis Rossi - was forced to cancel shows as he underwent tests for suspected throat cancer.
Status Quo, known for hits such as Whatever You Want and Rockin' All Over The World, first played together in the early 1960s.