Mexican Perez has been signed to replace 2008 world champion and F1's last-start winner Hamilton for 2013 and beyond.
Currently at Sauber, 22-year-old Perez has said his 2013 target is wins and the title, but in the five races since the McLaren deal was announced, he has failed to score even a single point.
"I have a feeling he will be competitive, but of course he doesn't have the experience and I don't think he will be fighting at the front at the start of next season.
"It is a massive ask but what else can you do? You need to have someone in the car and he is quick.
"I don't know if he will be up to it straight away but we might be surprised at the first race," added Button.
Perez acknowledges the doubters, but said it has little to do with his black run of form at Sauber since the McLaren deal was announced.
"I am going to the best team next year, so there will always be a question mark until I constantly deliver in a McLaren," he is quoted by the BBC. "This doesn't bother me."
But the BBC claimed Perez is currently a long way from McLaren's standards, having failed to come close to Hamilton and Button in the British team's benchmark fitness test.
"I am not worried about him," insisted team boss Martin Whitmarsh. "We have the winter to prepare him."