In a statement on social media, Ms Johnson said the brother or sister to their first child Wilfred was due to arrive “this Christmas”.
The 33-year-old environmental campaigner added: “At the beginning of the year, I had a miscarriage which left me heartbroken.
“I feel incredibly blessed to be pregnant again but I’ve also felt like a bag of nerves.”
The couple made the announcement only two months after they tied the knot during a low-key wedding at Westminster Cathedral.
Ms Johnson, a former Conservative Party communications director, said she wanted to share the personal news about her miscarriage to “help others”.
She added: “Fertility issues can be really hard for many people, particularly when on platforms like Instagram it can look like everything is only ever going well.
“I found it a real comfort to hear from people who had also experienced loss so I hope that in some very small way sharing this might help others too.”
Downing Street said the Prime Minister had been due to work this weekend from his official country residence Chequers in Buckinghamshire, although it is not known if the couple are there together.