The 25-year-old suffered the collision early in the opening period, and was subsequently replaced after just 25 minutes.
A club statement read: "Gerard Pique has been discharged from hospital after follow-up medical tests proved satisfactory.
"The Barcelona defender spent the night in hospital under observation after a heavy collision with Didier Drogba and Victor Valdes in the early stages of the match against Chelsea. The player will now rest for a week before being re-assessed."
Barcelona suffered a 3-2 aggregate defeat at the semi-final stage.