The setback comes at an inopportune time as coach Manuel Pellegrini looks to build on Real's positive display against leaders Barcelona at the Nou Camp on Sunday, when they were unfortunate to lose 1-0.
Barca are now five points clear at the top, having extended their lead with a midweek defeat of Xerez, in a game re-scheduled because of the Club World Cup.
Real had been boosted last week by the return of Cristiano Ronaldo after two months out with a twisted ankle, but now it is Kaka who is the cause for concern. The former AC Milan player has been training apart from the rest of the squad.
"He has been playing through the pain. He has had a groin problem and this perhaps explains his inconsistent performances," Real sports director Miguel Pardeza told Radio Marca.
"In my day it nearly always required an operation but now there are other types of treatments which are much better, and I am sure he will be back with us again very soon."
Pellegrini could rest Kaka with one eye on the last round of Champions League group stage matches next week.
Barcelona coach Pep Guardiola is also having to juggle his squad carefully, with the added complication of the upcoming Club World Cup which starts in Abu Dhabi next week.
SHAKY PERFORMANCE
The champions face a tough trip to play fifth-placed Deportivo La Coruna on Saturday after another shaky performance away from home against bottom club Xerez on Wednesday.
Substitute Zlatan Ibrahimovic's superb last-minute strike made the scoreline more respectable at 2-0 and ended a run of three consecutive away draws.
Guardiola admitted it had been a far from vintage performance although understandable so soon after the 'clasico.'
"This was a very dangerous game for us right until the end," he said.
"We became bogged down, we didn't move the ball about cleanly, and we were too slow. It's clear we weren't at our best."
Third-placed Sevilla are at home to Real Valladolid on Saturday while fourth-placed Valencia will need to be at their best to take all three points from Athletic Bilbao at San Mames on Sunday.
Atletico Madrid dragged themselves out of the relegation places with only their second win of the season last weekend, and have a good chance to climb further away from trouble at basement side Xerez on Saturday.
