Ismail Haniya was not in the office at the time of the attack, which took place shortly before 2am on Sunday.
Haniya visited the site of the attack shortly afterwards and called on the international community to end Israel's offensive.
A Palestinian was killed in another missile attack on a Hamas office in the northern Gaza Strip town of Jabaliya, witnesses said.
An Israeli aircraft also fired a missile at a Gaza school founded by the late Hamas spiritual leader, Shaikh Ahmad Yassin, witnesses said. There were no casualties.
An Israeli military spokeswoman confirmed that the air force had attacked Haniya's office, but had no immediate word on the other strikes.
Israel sent troops and tanks into the Gaza Strip after Palestinian fighters abducted one of its soldiers in a cross-border raid last Sunday.
Haniya(C) visited his office in
Gaza after the Israeli air strike
Civilian infrastructure and offices used by the Palestinian government have also be attacked by air strikes.
Ehud Olmert, the Israeli prime minister, said that the military was ordered to do "everything" in its power to return 19-year-old corporal Gilad Shalit and that arrests of senior Hamas officials could spread to Gaza.
Last week, Israel detained 64 Hamas leaders, including eight cabinet ministers, in raids in the West Bank.
"Wherever there is a proven terror infrastructure, there will be arrests. There will be immunity for no one," Olmert reportedly told his cabinet.
Amir Peretz, the defence minister, said Israel would go after "higher-calibre targets" in the future - a reference to senior Hamas officials inside and outside the Palestinian territories, a political ally said.
The men holding Shalit are thought to take their orders from Hamas's Damascus-based leader, Khaled Mashaal.
The ground invasion has focused on southern Gaza, where Israel believes Shalit is being held. On Sunday, officials decided to invade northern Gaza if rocket fire on southern Israel resumes from that area, security officials said.
The armed wing of Hamas responded to the air strikes by threatening to attack schools, institutions and power plants inside Israel.
"If they continue with these attacks we will strike similar targets in the Zionist occupation which we have not targeted until now," said Abu Ubaida, a spokesman for Hamas's Izz el-Deen al-Qassam Brigades.
The UN said Gaza could face
shortages because of the offensive
Mahmoud Abbas, the Palestinian president, toured Haniya's wrecked office with the prime minister. "The world must understand that this is a true criminal act," he told reporters.
Abbas's spokesman has insisted efforts to resolve the crisis by the Palestinian leader and Egypt are continuing.
"Efforts continue, but so far in vain. We are near an impasse," Nabil Abu Rudeina told reporters after a meeting in Gaza City between Abbas and United Nations Middle East envoy Alvaro de Soto.
Israel has rejected the demands of the three Palestinian groups that jointly admitted responsibility for capturing Shalit.
The Israeli's kidnappers issued a statement on Saturday demanding the release of 1,000 "Palestinian, Arab and Muslim" prisoners in exchange for Shalit.
A UN official said widening the Israeli offensive to the northern Gaza Strip could displace up to 25,000 Palestinians.
There are concerns of a humanitarian crisis if the offensive continues to affect food and medical supplies to the Palestinians.