The ex-Arsenal and Tottenham stopper was in the England squad for six major tournaments and thinks manager Roy Hodgson should opt for experience at centre-back in the form of Gary Cahill and Chris Smalling.
Campbell feels Stones, 22, is still learning the game and the unforgiving nature of a European Championship would not be the right place for him to make the mistakes that naturally come with a young player's development.
The Barnsley academy graduate struggled to hold down a place in Everton's first team last season after making several high-profile errors, prompting concerns over how he will fare if called upon in France.
"I personally would go for Smalling and Cahill - I would go for the experience of those two guys," Campbell told reporters at a William Hill event.
"For me, something drastic would have to happen for Stones to start. You start with your most solid back four and go from there.
"If you keep making mistakes at international level, you are going to suffer because one mistake in a tournament and you can be out.
"If you make mistakes at a domestic level, you have more time to learn and he is learning.
"He just has to understand there are moments to play the ball and moments to keep hold of it. He just needs to find that balance."
Campbell was part of England's squad that made the semi-finals of the Euros in 1996 on home soil and he feels the last four should be the minimum target for Hodgson's team in France, although he has confidence they can even go one step further.
"I think England will get to the final, I really do," he said.
"Success for Hodgson is semi-finals plus. You have to look at what he has done, he ticks a lot of boxes for the FA, but he has to at least take England to the semi-finals.
"You need to see progression and this England squad, which is an exciting squad, deserves progression in all departments."