Djokovic, the world number two on a mission to topple Rafael Nadal, has had problems with his right hand since the Monte Carlo Masters in mid-April.
Kolar, who first treated Djokovic last year for an ankle injury, said the Serbian six-time Grand Slam champion was suffering from an inflamed tendon.
"The treatment took place last week but we agreed he would resume training gradually, slowly, to avoid a recurrence," he said.
"Madrid was too early, he would have to start playing on clay which is far more demanding than other surfaces, you play more returns and more spins, straining your wrist, so we decided he would come back in Rome."
The French Open, which starts on May 25, is the only major Djokovic has yet to win.