She has hinted at her desire for another child and was reported two weeks ago as saying she would love another child to keep Lourdes company.
A statement released by the 41-year-old singer ended weeks of speculation that the couple were expecting a child.
It said they were "happy to confirm rumours" that Madonna was pregnant.
"We would be grateful if the media would kindly allow us some privacy at this special time and we thank you all for your good wishes," the statement added.
Madonna has a three-year-old daughter, Lourdes, whose father is former fitness instructor Carlos Leon.
The singer recently confirmed she was in a "serious relationship" with Ritchie, 31, the British director of the film Lock, Stock and Two Smoking Barrels.
She has hinted at her desire for another child and was reported two weeks ago as saying she would love another child to keep Lourdes company.
She said: "I would love to have another child but I don't know for sure. I am definitely interested, but I don't know whether it will happen."
The star was briefly married to actor Sean Penn before having a baby with Leon, whom she never married.
They split up when Lourdes was about 18 months old.
The announcement came shortly after Madonna recorded another number one hit in the British charts with her cover of Don McLean's "American Pie".