Brooks was arrested after an Oct. 14 incident in which his male roommate accused him of assault. No injuries were reported.
City spokeswoman Sarah McKenzie said in a statement that the investigation has been completed and there is insufficient evidence to prove the case beyond a reasonable doubt.
Brooks, who suffered a torn anterior cruciate ligament in his left knee before the season, was cleared to play on Oct. 20, but he was suspended for that game following his arrest.
He returned to the field last Friday and had 154 yards and a touchdown on 22 carries in the Gophers' 38-31 win over Indiana, before he hobbled off the field with an injury to his right leg.