The German is undergoing surgery to repair the break on Sunday.
On Twitter, Greipel said it was "not the way I wanted to finish my Milan-San Remo", and lamented that the crash with 4km to go left the team without the result they worked for.
Jasper De Buyst, in his first Milan-San Remo, said on Twitter that his front wheel slipped away on the descent of the Poggio, leading to the crash with Greipel.
The crash happened off-camera, unlike the dramatic fall from Mark Cavendish (Dimension Data), who struck a bollard on the run-in to the Poggio, suffering a broken rib, scrapes and bruises, according to his team.
Cofidis' Anthony Turgis and Guillaume Bonnafond were caught up in the crash with Cavendish. Turgis suffered a broken collarbone while Bonnafond finished the race with multiple contusions.
EF Education-First Drapac had three riders go down in two incidents. Mitch Docker crashed along with Lukasz Wisniowski (Team Sky)in the feed zone, with both abandoning the race.
In a later incident, Simon Clarke and Dan McLay crashed together on a descent with roughly 45km to go. Clarke hit a stone wall, stating later on Twitter, "Unfortunately I have 3 broken vertebrae from my crash in MSR today. On the bright side, enjoying a pizza in the back of the ambulance."