Santana went on the 15-day disabled list with inflammation in his back.
Alderson said rookie right-hander Collin McHugh will take Santana's place in the Mets' rotation, MLB.com reported.
Santana, in his first season back from left anterior capsule shoulder surgery, experienced back stiffness following a bullpen session this week. A magnetic resonance imaging test revealed damage, which prompted the Mets to shut the left-hander down, MLB.com said.
Santana, a 33-year-old, two-time Cy Young winner, was 6-9 with a 4.85 earned run average in 21 starts this season. He threw a no-hitter June 1 against St. Louis, but had not won since June 30 at Los Angeles.