It followed a march by Jewish nationalists in occupied East Jerusalem on Tuesday, which had drawn threats from Hamas, the militant group that runs Gaza.
Explosions in Gaza early Wednesday morning.
The strikes were the first under the new coalition government headed by Naftali Bennett, who took over on Sunday after ousting former prime minister Benjamin Netanyahu.
The US and United Nations had called for restraint before the march, which the government of new Israeli Prime Minister Naftali Bennett had authorised.
The "Harvard Israel Initiative", which as of Tuesday afternoon had garnered 905 signatures and counting, asserts Israel's "right to self-defense" and the "right of the Jewish people to self-determination", while "condemn [ing] in the strongest of terms the indiscriminate firing of rockets by Hamas, a USA -designated terrorist group, at Palestinian and Israeli civilians".
Hundreds of Israeli ultra-nationalists paraded through the Old City, celebrating Israel's capture of East Jerusalem in 1967.
The Israeli military says the attack was a response to incendiary balloons that caused fires in fields in southern Israel.More news: Bidens to have tea with Queen Elizabeth as G7 ends
Police said that officers arrested 17 people suspected of involvement in violence, some of whom threw rocks and attacked police, and that two police officers needed medical treatment.
Yair Lapid, the architect of the new government, tweeted he believed the march had to be allowed but that "it's inconceivable how you can hold an Israeli flag and shout, "Death to Arabs" at the same time".
Israeli media reported that police will allow participants to congregate outside the Old City's Damascus Gate but will not let them cross through it to the Muslim Quarter, which has an overwhelmingly Palestinian population.
More than a thousand ultranationalist demonstrators bearing Israeli flags poured into Jerusalem's flashpoint Old City on Tuesday in a march that posed a key test to Israel's new government on its second full day in office.
"I got the impression that the police are well-prepared and a great effort is being made to preserve the delicate fabric of life and public security", Bar-Lev said.
The rescheduled event was initially planned for last Thursday, but was postponed to this Tuesday when police refused to authorize its planned route through the Old City's Damascus Gate entrance and Muslim Quarter.
Hamas had called on Palestinians to show "valiant resistance" to the march.More news: Annular Eclipse Brings 'Ring of Fire' to Northern Hemisphere on June 10
According to Palestinian sources, Israel's air force targeted at least one site east of Khan Yunis in the south of the Gaza Strip, which is home to some two million people.
During May's 11 days of cross-border violence, more than 240 people were killed in Gaza and at least 12 were killed in Israel.
The demonstration triggered protests in the West Bank and Gaza Strip and prompted rebukes and warnings from Israel's allies.
New Public Security Minister Omer Barlev said Monday that the march will proceed as scheduled, following a meeting with Israel Police Chief Kobi Shabtai on preparations for the march.
After capturing east Jerusalem in 1967, Israel annexed it in a move not recognised by most of the worldwide community. He "underscored the need to avoid friction and protect the personal safety of".
"Urge all relevant parties to act responsibly & avoid any provocations that could lead to another round of confrontation".More news: Biden withdraws Trump-era executive order that attempted to ban TikTok, WeChat