The 48-year-old told the New York Times: "I'll be showing soon."
Ms Weisz said she and Bond star Craig, 50, who married in 2011, are delighted and added: "Daniel and I are so happy. We're going to have a little human.
"We can't wait to meet him or her. It's all such a mystery."
The Mummy star has an 11-year-old son from her relationship with director Darren Aronofsky.
Craig has a 25-year-old daughter from his previous marriage to actress Fiona Loudon.