Parfitt, 48, from Teddington, south-west London, was recovering in the intensive care unit at London's Wellington Hospital after a four-hour operation.
A spokesman for the band said: "He is drifting in and out of consciousness but he has been talking to nurses. He's desperate to get back to work but surgeons say he will have to wait until 1 August."
The musician was admitted to hospital after complaining of chest pains. Extensive tests revealed a narrowing of arteries to his heart, and his surgeon recommended immediate surgery. He is expected to make a full recovery but will remain in intensive care until this evening.
His manager, David Walker, arrived at the hospital in St John's Wood yesterday afternoon. He said Parfitt had the first twinges of pain on Sunday, but it was not until Tuesday, after he had finished a day's recording that he contacted his Harley Street doctor.
"Rick woke up in a state of shock. He was all wired up and drugged up but he still had a smile in his eyes," said Mr Walker. "He had shown no signs of heart problems during the extensive tour in which we covered between 40,000 and 50,000 miles. He had only complained about the usual things, such as tiredness.
"He went to his doctor, who had experienced similar symptoms and had the tenacity to recognise that Rick would need thorough tests.
"I was told on the phone that the tests would be a safety precaution, but then I got a message from his surgeon saying that unless he went under the knife immediately, it could be too late."
Mr Walker added: "We have no idea what caused this, after all he keeps fit. The show itself is a keep-fit show. I guess it was to do with smoking and a bad diet, though I tried to get him to use patches to get him off the cigarettes."
The operation has caused the immediate cancellation of all Status Quo concerts for May, June and July. The band was due to undertake a series of 21 European and festival appearances this summer, playing to more than 1 million fans.
Last year Parfitt crashed his Porsche and was banned from driving for 18 months.Reuse content