Sterling returned to his club at the start of the week after pulling out of Gareth Southgate's latest England squad with what was described as a “small" injury.
But Tottenham boss Mourinho suggested Sterling's injury was not genuine and called on Southgate to name and shame managers who get their players withdrawn from England duty with bogus problems.
That drew a withering response from Guardiola, who said: “Mourinho has to speak to the doctor for the national team of England and the doctor for Manchester City.
“He has to go to the doctors of the national team and Manchester City. Except maybe Mourinho is a doctor, I don't know."
When Guardiola was later asked about Mourinho's insinuation that City's players go down too easily when fouled, the Spaniard said: “Listen, I'm not going to answer anything about Jose.
“I said about the doctor, because he accused us of something we've done that is not true.
“You have to speak to the doctors about these other things, don't ask me. I'm almost 50. I'm old enough to understand."