The British group, known for hits such as Whatever You Want and Rockin' All Over The World, had been due to play in Croatia tonight.
However, it is one of six shows on the current leg of their European tour to be shelved while Parfitt is assessed in a hospital in Pula in the northern part of Croatia.
The band's manager Simon Porter said: "The band do not cancel shows lightly, as any of our fans will tell you, but in this instance we have no option but to follow medical advice."
Little has been disclosed about the nature of Parfitt's condition, although a spokesman said the band will release more information on his condition when it is known next week.
It is not known whether or not the band's UK tour, scheduled for December, will be affected.
The band's dates in Monte Carlo, Switzerland and Germany - up until August 10 - have been cancelled on medical advice.
In 1997, 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 currently hold the record for the most British singles, at 64.