Kyrgios had been under a fitness cloud having not played a singles match for six weeks and returning home last month for cortisone treatment for the chronic injury.
The 23-year-old on Saturday said he remained only "about 80 per cent" fit after teaming with American Jack Sock to land his maiden ATP doubles crown in Lyon.
He went behind closed doors for a practice session with Sock at Roland Garros on Sunday before pulling the pin.
Unfortunately, I have to withdraw from this year's French Open," Krygios tweeted.
"Having consulted with my team and medical experts it is deemed too risky for me to step out and potentially play five sets on clay especially as I have not played a singles match in nearly two months.
"I've worked hard to be ready and desperately wanted to play Roland Garros, which is very special to me but I literally ran out of time."
"A dramatic spike in load on my elbow could potentially put me back to square one and with the grass court season around the corner, it is something I can not and will not risk.
"The good news is I'm finally pain-free, working hard and enjoying my training and I'm looking forward to being back in singles action in Stuttgart.
"I'm sorry to those fans who bought tickets to watch me play but am also grateful for the continued love and support."
Kyrgios's scratching leaves Tomic, who successfully qualified after missing direct entry, to face lucky loser Marco Trungelliti on Monday night.
Should Tomic win his opener, the world No.206 will play either Romanian Marius Copil or Italian Marco Cecchinato for a place in the last 32 in Paris for the first time.
