The 31-year-old from Luxembourg said she and her husband Tim Sommer had always wanted children but had planned to start a family after her playing days were over.
"We were very happy with the news, but we will have to adjust," she told a small group of reporters on Thursday.
Minella said she found out she was pregnant just before going out to face Svetlana Kuznetsova in the first round in Miami in March.
"It was a real shock. My whole body was sweating and I was shaking but we were happy straight away.
"We always wanted to have a family and that is a great moment that will stay in our memory for ever."
Minella joins a growing list of tennis mums.
Former world No 1 Victoria Azarenka is playing Wimbledon six months after giving birth to son Leo.
Serena Williams, meanwhile, is expecting her first child in August.
