The Brit has enjoyed a strong start to the campaign, following up a fifth-placed finish in the Australian Grand Prix by coming third in Malaysia a week later.
Hamilton's and Mercedes's chances of success were written off during the winter break, but the former three-time world champion believes that both can race to title victories this year.
"Yes, they can win races. Lewis will drive the living daylights out of whatever car he's got," Stewart told BBC Sport. "They can challenge for the title but they will need to keep up with Red Bull and Ferrari in terms of development.
"If the Red Bull is as good as it can be, that's your main opposition while Ferrari are already more competitive at the start of the season than they were last year.
"The Lotus is very competitive, too, and McLaren will fight back, but [Mercedes team principal] Ross Brawn is an extraordinarily talented man. Mercedes exist to win and they have the resources to do so."
Hamilton joined the Silver Arrows this year after spending six seasons with McLaren.