According to reports, no one was hurt in the bombings, and a group calling itself the Sword of Islam has claimed responsibility for the blast.
The explosions took place at about 3am local time, Palestinian authorities have said.
The Islamic group has claimed responsibility for a number of similar attacks on public areas in recent months.
Officials refused to speculate on the identity of those behind the attacks, simply saying that investigations were ongoing.
The damaged bookstore was funded by American Protestants and known as the Bible Society. It sold Christian books exclusively.
Over the past few months, about three dozen internet cafes and shops selling pop music have been attacked in the Gaza Strip, causing damage but no injuries.
