"It's nothing to worry about. He has played a lot this season, so we have decided to give him some rest," chief selector Dilip Vengsarkar said.
All-rounder Irfan Pathan, who is nursing a shoulder injury has not recovered fully and is unlikely to play in fourth and final one-dayer, confirmed team sources.
The series is currently tied at 1-1, with one match abandoned due to rain.
Tendulkar, plagued with fitness problems in recent years, missed a home one-day series against England and then the West Indies tour last year because of a shoulder injury.
But the master batsman said the latest problem was not a great concern.
"It (the back) is just stiff. Nothing serious," said Tendulkar, the world's leading scorer in one-day internationals with 14,783 runs and a record 41 centuries in 381 matches.
Tendulkar has been playing regularly since returning to the squad last August and the hectic schedule seemed to have taken its toll.
The ace batsman, who suffered a back injury in 1999 during the home series against Pakistan, was reported to have had the same problem during the five-day final of the premier domestic tournament early this month.
But he showed no signs of it, scoring 105 and 48 against Bengal to help Mumbai win the Ranji Trophy.
Indian cricket board secretary Niranjan Shah said the team management had requested that Tendulkar be rested for the Visakhapatnam game on Saturday.
"This was done after a check-up by team physio John Gloster," he said.
India are also concerned over the fitness of pacemen Irfan Pathan and Munaf Patel, and all-rounder Yuvraj Singh, who are all returning from recent injuries and are expected to play big roles in the World Cup, starting in the Caribbean next month.