The 155-pound fight was supposed to headline UFC Fight Night in Sioux Falls, South Dakota. The UFC has not announced a new plan for the televised event.
Chiesa acknowledged having a "fully ruptured disc" in a Facebook post Monday.
"I will undergo 8 weeks of physical therapy and rehab to hopefully avoid having to go under the knife and get back surgery," he wrote.
Chiesa (14-2) was looking to build on a three-fight winning streak. A former winner of The Ultimate Fighter Reality series, Chiesa is 7-2 overall since signing with the UFC in 2012. There is currently no timeframe for the 28-year-old's return.
Ferguson (20-3) has won seven in a row and is closing in on title contention. A former TUF winner as well, Ferguson was originally scheduled to fight Khabib Nurmagomedov in April, but was forced to pull out of that bout due to blood in his lungs. ESPN.com ranks Ferguson the No. 4 lightweight in the world.