Nine of the injured were in a house that was struck in an air raid on the southern city of Khan Younis, said Asraf al Qedra, emergencies' spokesman in the Gaza Strip.
"The Israeli Defence Forces have launched Operation Protective Edge against Hamas in Gaza to stop the terror that Israeli citizens face each day," said an IDF spokesperson on his official Twitter account late Monday.
In a later statement, Israel announced that the attack began with aerial and naval artillery strikes against 50 targets of the Islamists in Gaza, including rocket launchers, tunnels, arsenals and training centres.
The Israeli army said about 200 rockets had been fired from Gaza since June 12, when Israel began a massive search for three Jewish seminar students who went missing in the West Bank and were found murdered last week.
Israel blamed the kidnappings on Hamas, which has denied any role in the deaths, and arrested 500 people, most of them linked to the Islamist movement during the search.
Israel has responded to the rocket attacks from Gaza with air strikes that have caused the death of 11 Palestinian militants, including six Hamas members, and a seven-year-old boy, and injuries to dozens of people, most of them civilians.
The two sides were on the brink of a major conflict after the Al Qassam Brigades, the Hamas's military wing, announced Monday night it had fired a new barrage of rockets at Israel, and after the government of Benjamin Netanyahu decided to increase its attacks on the Gaza Strip.
Tensions have flared after a Palestinian teenager was bundled into a car in Jerusalem last week and found burned to death hours later in a revenge killing for the murders of the three Israeli students.
Israeli security forces have arrested six people in connection with the murder, one of whom Monday confessed and also confirmed the involvement of the other accused.
Ismail Haniyeh, the deputy chief of Hamas's Political Bureau, Tuesday called on the Palestinian people to stand united in the face of Operation Protective Edge.
Haniyeh said in a press statement that cooperation between Palestinians was necessary to cope with this "critical stage".