“I’m trying to be very patient. But we are good and just waiting a little bit.
“We have a few tests in the next few days and then we will see how the injury is and what the next steps will be.”
The 22-year-old, who won clay-court titles in Monte Carle, Rome and Roland Garros and reached the final in Barcelona last season, could lose significant ground to Sinner in the rankings because of the injury.
Italian Sinner reclaimed the number one ranking this month after beating Alcaraz in the Monte Carlo final.
Alcaraz said: “I’d rather come back a little later but in great shape than come back early, rushing around, and unwell.
“God willing, I have a very long career ahead of me, many years, and pushing myself too hard at this Roland Garros could seriously harm me in future tournaments.
“Things happen in the professional world. You have to accept them. I need to recover really well if I don’t want it to affect me later on.”
