Former world champion Hamilton has begun a new era in his F1 career at Mercedes after six seasons with McLaren, a team he initially joined at the age of just 13.
And Stewart is hoping the 28-year-old does not let his focus drift elsewhere.
He said: "If I had been Lewis, I would not have left McLaren. But, as a 28-year-old, he should know what he is doing now.
"You just have to be damn careful you don't get carried away with your own importance, your own celebrity, or your own schedule outside of being in the cockpit. It can be quite intoxicating.
"It's about who you hang out with, what you do in your off time, how you are committing your off time towards your real time – and your real time is being a racing driver."