The 25-year-old picked up the injury in his club side's 15-15 draw with Ospreys in the European Champions Cup on Saturday evening, forcing him to make way midway through the match.
Vunipola played on for the final stages of the first half, offering hope that the damage - sustained in a challenge with Ospreys' Rob McCusker - was not too serious.
Saracens have confirmed that the England international is facing a prolonged spell on the sidelines, however, effectively ruling him out of the Six Nations, which begins in less than three weeks' time.
"Saracens can confirm that as a result of an injury sustained in Saturday's European Rugby Champions Cup match against Ospreys, Billy Vunipola has fractured his forearm," a statement read. "Vunipola had an x-ray today (Sunday) confirming the injury.
"Billy is due to see a specialist later this week, when a timeframe for recovery may be defined. But until that time Saracens will make no further comment. Saracens will issue a further statement once Billy has seen a specialist."
Vunipola had only recently returned to action following a knee operation last summer.