The Rapids could now turn to Clint Irwin at goalkeeper, who made his MLS debut in relief of Pickens on Saturday.
He will now miss 3-4 months after undergoing surgery Saturday night.
The injury occurred early in the match after a collision with RSL defender Kwame Watson-Siriboe. Pickens was immediately removed and replaced by Clint Irwin, who played the rest of the game in an eventual 1-1 draw.
The 23-year-old Irwin appears in line to take the first crack at starting duties for the Rapids, as former backup Steward Ceus has fallen to third string after an error cost the team a goal in a season-opening 1-0 loss to FC Dallas.