The bombing began late in the evening, the Jerusalem Post reported. Earlier, the Israeli military said it shelled two targets in Gaza.
Islamic Jihad said three of its members were killed Tuesday by an Israeli airstrike. The Israeli military said its attack was launched because the group was firing mortar rounds across the border.
Officials said the attack Wednesday evening from Gaza was the biggest since 2012. At least 30 rockets fired from Gaza struck Israel, including eight that hit civilian urban areas. A police representative said one missile struck in Sderot.
The newspaper said Israel Radio reported as many as 55 rockets had been lobbed into Israel.
Palestinian media reported Islamic Jihad had claimed responsibility for the attack.
Meanwhile, Israeli security and police officials said Wednesday they had arrested a Palestinian suspected of cutting cooking gas pipes in residential buildings in Jerusalem.
The suspected gas line terrorist was identified as Aziz Musa Uwisat, 48, of Jabel Mukaber, the Jerusalem Post reported. Uwisat, who holds an Israeli identification card, was also suspected in a 2012 knife attack.
The newspaper said Shin Bet, Israel's security agency, alleges Uwisat confessed during interrogation he sabotaged gas pipes in February and March in unsuccessful attempts to kill as many Jews as possible in retribution for Israel's killing of people in the Gaza Strip. He allegedly said he got the idea after a deadly gas line explosion in January.
"His motive was nationalistic, that is certain," a security source told the Post.
In the most recent incident, police said residents of Armon Hanatziv last week reported leaking gas and two gas lines to their building were found to have been deliberately cut.
"The pipes were intentionally cut which caused extreme danger, so police evacuated three buildings in the area and shut off the gas supply," a police official said at the time.
"Thankfully, we managed to prevent an explosion."