The James Bond star - who tied the knot with Weisz last month - insisted that it is "incredibly important" for him to keep his private life out of the media.
He told Access Hollywood: "I did it secretly - I can't tell you how I pulled it off. My private life is incredibly important to me, and certainly that aspect of it is more than incredibly important to me."
The actor's friend Jason Isaacs recently said that Craig is "very happy" in his marriage.
Craig and Weisz - who star in horror movie Dream House together - began dating in December and got married in front of just four people.
The actress split from director Darren Aronofsky last year. They have a 5-year-old son Henry together.