The news will come as a further blow to the hosts who have already lost the series after big defeats in Galle and Colombo.
The 39-year-old Herath has carried a heavy workload in recent weeks, first bowling 71 overs in the one-off Test against Zimbabwe then sending down a combined total of 91 overs in the first two matches against India.
Herath’s back problem is thought not to be serious but he is just being rested as precaution.
Sri Lanka cricket manager Asanka Gurusinha said: “This is where our player management comes in, because we don’t want to break anyone.
“We made the call not to risk Herath because he’s also bowled close to 200 overs in the three Tests. That’s a lot for his body.”
Herath is the now the fourth player to become unavailable during the India series after allrounder Asela Gunaratne and seamer Nuwan Pradeep were ruled out due to injures while Suranga Lakmal also has a back ailment.