Anderson withdrew from the Monte Carlo Masters last week due to an issue which also kept him out of the hard-court events in Acapulco and Indian Wells.
The 32-\ year-old South African, runner-up at Wimbledon last year, revealed that he will focus on getting fully fit for the grass-court season.
"I wanted to let you all know that I will unfortunately be missing the clay season this year," he tweeted. "After discussing with my doctors and team, we thought the best decision is to rest and rehab my elbow injury for a few more weeks. I will keep working hard each day to get healthy again in time for grass.
"I'm very disappointed to be missing Estoril, Madrid, Rome and Roland Garros - all incredible events that have been so great to me and I love going back to - but I know this is the right decision for the long term in my career."
Anderson has played in only three tournaments this year, winning the first one he entered in Pune.