Carroll is in contention to start against France when England kick off their campaign, with talisman Wayne Rooney banned for the first two group games. The Liverpool man became the most expensive English player of all time when he signed from Newcastle last year, and despite a difficult start, Shearer thinks he can succeed for his country this summer.
"The ability's there. I saw that at Newcastle," he told ESPNStar.com.
"He's had an in-and-out season but, for the last month, you've probably seen more of what Andy Carroll is about.
"If you've got him in your team, you've got him in your team for one reason, and that is to get balls into the box. Because, if you get the right balls in, not many people will be able to stop him.
"If you do that, he'll score goals, whether that's at club level or international level. He could play with most players. He could play with Wayne.
"I hope he gets his opportunity to do that. I hope they get through and they're able to do that."
Shearer added that if he were picking the squad to take to Ukraine and Poland, Rio Ferdinand would be playing, and that he believes England will have done well if they reach the semi-finals.
He added: "If it was my decision then I think Rio still has a lot to offer.
"I suspect it might be the end of him now if [Hodgson] hasn't picked him for this tournament because of form.
"He's had a few injuries but I don't think you can doubt his ability.
"I think we'll do well if we get to the semi-final. I've not met anyone who says we can win it, which hopefully can work in our favour.
"For the first time in a long time, there's no huge pressure for them to win it. One thing that will happen is that England will be well organised. They'll be well drilled.
"Chelsea were that in the Champions League, weren't they? And if you're hard to beat then you can always nick a goal."