Gayle, who missed his side's final pool game against United Arab Emirates with the injury, was now almost certain to play in the cricket World Cup quarter-final at Wellington Regional Stadium.
"I think yesterday he had a scan. He had an injection," the 31-year-old Sammy told reporters on Wednesday.
"Chris is not missing this quarter-final for anybody. He is more pumped up for this than the rest of the team.
"It's just unfortunate his back keeps hindering his progress but he won't miss the quarter-final."
West Indies lurched into the quarter-finals and only qualified for the knockout stages on the final day with a six-wicket victory over United Arab Emirates in Napier.
Sammy drew a lot of smiles on Wednesday when he claimed his team were the underdogs, yet it was his comparison of Brendon McCullum's side to another sportsman that drew a few chuckles.
"It's a big match, and I remember some guy named (Buster) Douglas beating Mike Tyson so it's the case of that on Saturday," he added.
"It's the business end so you can win all your pool matches and come in the knockout there is no guarantee you will win.
"You turn up on the day and the guys know what is at stake and we are doing everything in our powers to beat Mike Tyson."
Comparing New Zealand to Tyson, the former undisputed heavyweight boxing champion who suffered a shock loss to Douglas in 1990, will no doubt also cause a wry smile amongst the management of the New Zealand cricket team, who are often categorised as the underdogs in most matches they play.
Brendon McCullum's team, however, went through the pool phase unbeaten and their aggressive style of play has drawn plaudits from around the cricketing world.
Sammy was honest about his team's inconsistent performances so far, but said they had still achieved their first goal of making the knockout phase and would look to push on beyond Saturday's clash.
"We're not supposed to be here. We have not played our best cricket," he added. "We have been so inconsistent but we are still in the quarter-finals.
"If we put all the good things we know we can do right then no team will beat us.
"And the other teams know that as well."
(Reporting by Greg Stutchbury; Editing by Julian Linden)
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