At a press conference to preview the tie in Constanta, which starts on Saturday, Romania's captain was heard to say of Williams' baby, due in the autumn: "Let's see what colour it has. Chocolate with milk?"
Williams announced on Wednesday she is expecting her first child with fiance Alexis Ohanian, who is white, and will take time away from the tour.
Nastase was not asked about Williams himself but made the comment, in Romanian and clearly audible, to the other players while Romanian number one Simona Halep was answering a question about the 23-time grand slam singles champion.
The International Tennis Federation (ITF) has launched an investigation and said in a statement: "The ITF does not tolerate discriminatory and offensive language and behaviour of any kind.
"We are aware of alleged comments made by Romanian captain Ilie Nastase and have begun an immediate investigation so that we have the full facts of the situation before taking further and appropriate action."
The Romanian tennis federation, of which Nastase is a former president, declined to comment.
These are the second controversial remarks made by Nastase, who was appointed Fed Cup captain in October, about Williams in a month.
In an interview with Romanian media, the former world number one made totally unsubstantiated allegations of doping by Williams based purely on her physique.
Nastase was appointed captain of the Romania team in October and is a former president of the country's tennis federation.
The 70-year-old, who had a reputation as a playboy during and after his playing career, also clearly made Great Britain captain Anne Keothavong feel uncomfortable with a number of inappropriate remarks.
Having asked for her room number during the official dinner on Thursday, Nastase then repeated the request when the captains posed together for photographs following Friday's draw and put his arm tightly around Keothavong's shoulder.
When both teams were called back together, Nastase said to Keothavong, who is married and 18 weeks pregnant with her second child: "We keep being attracted."
The tie begins on Saturday at the Tenis Club IDU, with Halep taking on Heather Watson before Johanna Konta faces Irina-Camelia Begu.