Stokes was bowling to Tim Southee at Hagley Oval in Christchurch when he pulled up and tossed the ball to Gus Atkinson to finish his over.
Stokes stayed on the field and said after his side's eight-wicket win that stopping to bowling had been a precautionary measure and he would play in the second Test.
"I twinged my back diving for a catch on day one and there's a bit of stiffness," Stokes said after England easily chased 104 to beat New Zealand on the fourth day.
"Where we were in the game it was 'I don't really need to do this and put myself at risk'.
"So yeah, it was more for caution than anything else and I'll be fine for Wellington."
Stokes bowled four overs at the start of Sunday's fourth day before stopping after three balls of his next over, ending with figures of 0-30 off 6.3 overs in the innings.
He took 1-59 off 13 overs in the first innings and his match total of 19.3 overs were the most deliveries the injury-prone Stokes had sent down in a Test since playing in Pakistan in December 2022.
Atkinson dismissed Southee two overs later, New Zealand were bowled out for 254 and England blasted the 104 runs they needed for victory in just 12.4 overs after lunch.
The second Test starts in Wellington on Friday. The third and final Test is in Hamilton, beginning December 14.
