Police said the grenade, fired from a nearby highway, apparently did not explode after breaking through the cell window.
The injured biker was identified as Paul Andersen, who is being held pending trial in connection with the October anti-tank grenade attack on the Hell's Angels' compound in Copenhagen, Denmark, in which two people were killed and 19 injured.
Police said several people with ties to the Hell's Angels were arrested in connection with yesterday's 4am attack on the jail in Koege, 12 miles south of Copenhagen. They did not give further details.
The Hell's Angels and Bandidos gangs have been feuding for three years in Denmark, Finland, Norway and Sweden.
The gang war has left 10 people dead and more than 50 injured. Attacks have become increasingly brazen in the past year, beginning with shootings in March at the international airports in Copenhagen and Oslo, Norway, in which one Bandidos member was killed and four were injured.
Yesterday's attack was the first time in the feud that an anti-tank grenade was used against the Bandidos. At least nine grenades have been launched against the Hell's Angels or their allies.
Police said the grenade fired yesterday was of unspecified Eastern European origin. Officials have said that grenades used in previous attacks were believed to have been stolen from lightly guarded military depots in Sweden.