Rice was withdrawn on 72 minutes in England's opening game in Group L as the Three Lions eased to a 4-2 victory over Croatia in Arlington.
The Arsenal star has since confirmed he's managing a long-standing hamstring issue, but confirmed there's no concern over his participation against the Black Stars, in a major boost to Tuchel's plans.
The 27-year-old featured in all eight of England's qualifiers on route to the World Cup and he's unmoved in the engine room alongside Elliot Anderson.
Carragher is relieved by the positive news on Rice, but advised Tuchel not to risk his Gunners teammate Bukayo Saka, as he works his way back to full fitness in the USA.
"You don't rest when you're at the World Cup. If England win vs. Ghana, maybe you can do that in the third game, if you're guaranteed top spot. I don't think you're in a situation where you rest Declan Rice," he told Sky Sports.
"I think that was a precaution rather than an injury Tuchel's decision to take Rice off vs. Croatia. It's something he's been carrying for a lot of the season. He's been one of the best players in the league and it hasn't affected him too much at Arsenal.
"The fact Saka didn't start the first game means his injury is probably a little more serious than Rice's. He missed a lot of football last season and I don't think you risk him, because you don't want to lose him for the tournament. But the longer the tournament goes on without him starting a game, it's very difficult to expect him to come in for the knockout games and be at his absolute best."
Tuchel is expected to stick with Noni Madueke as a starter over Saka against Carlos Queiroz's team, but he faces crunch decisions over retaining John Stones and Anthony Gordon.