"My one request is that the media not send paparazzi to follow me or buy independent paparazzi photos, hence encouraging them.
"I want to remain peaceful during this very early time in my pregnancy and getting chased around by cameras is not in the doctor’s orders."
The news comes just two weeks after Alec, 61, hinted that the couple were trying for another child.
“We have four kids. She wants to have another one. We’re having another one. We’re going to have a fifth baby,” he confessed on Kevin Nealson’s ‘Hiking with Kevin’.
Alec and his yoga instructor wife share daughter Carmen, six, and sons Rafael, 4, Leonardo, 2, and Romeo, 15 months. Alec also has 23-year-old daughter, Ireland Baldwin from his previous marriage to Kim Basinger.
The baby reveal comes just five months after Hilaria broke the news that she had lost her baby, after revealing on social media that she was 'likely suffering a miscarriage'.
"I am surrounded by such love and I feel so fortunate. Thank you all for listening, for your support, and for sharing your own personal stories. We are stronger together..." she wrote at the time.