Local residents said an explosion, shortly before dawn, at the Protestant Holy Bible Society in Gaza City, blew out windows and ignited a fire that burned shelves of books.
Elsewhere in Gaza City, a bomb destroyed an Internet cafe, police said.
At least 3,000 Christians live among the 1.5 million Palestinians in the mainly Muslim Gaza Strip.
Relations between Muslims and Christians in the territory have been good.
The bombings came a day after the Palestinian cabinet agreed a security plan aimed at stopping mounting lawlessness in the Gaza Strip, where rival factions have frequently clashed.
Ismail Haniya of Hamas, the Palestinian prime minister said the new administration was determined "to end security anarchy".
The security plan sets up a liaison mechanism for rival security forces in a new push to promote law and order.
Haniya said he hoped cooperation among the factions would help end abductions of international journalists and aid workers.
BBC reporter Alan Johnston was seized in Gaza a month ago.
No one claimed responsibility for the kidnapping and there has been no confirmation on his whereabouts.