Palestinian officials said two people were hurt as sites belonging to Hamas, Islamic Jihad and the Popular Front for the Liberation of Palestine were hit.
Shells also reportedly damaged a water tower in the town of Beit Hanoun.
Earlier, a rocket launched in Gaza landed near a house in the Israeli town of Sderot without causing any injuries.
Israel and militants in Gaza led by Hamas, which dominates the coastal territory, fought a 50-day war in the summer of 2014.
Since then, a ceasefire has largely held, but some small jihadist groups have defied the agreement and periodically fired rockets at Israel.
A senior Israeli military official told the Haaretz newspaper that "dozens" of strikes on Sunday night had targeted Hamas "infrastructure".
"The attacks were out of the ordinary, but there is no intention to escalate the situation," the official added.
Military spokesman Lt Col Peter Lerner said it remained "committed to the stability of the region and operated in order to bring quiet to the people of southern Israel".
Hamas spokesman Sami Abu Zuhri said: "We hold [Israel] responsible for the escalation in the Gaza Strip and we stress that its aggression will not succeed in breaking the will of our people and dictate terms to the resistance."
Hamas leader Mahmoud al-Zahhar later blamed "a group not committed to the principles of the resistance of the occupation" for firing the rocket at Sderot.
Haaretz identified the group as Ahfad al-Sahaba-Aknaf Bayt al-Maqdis, which it said was affiliated with Salafist groups that identify with so-called Islamic State (IS).
The Israeli military says its aircraft and tanks attacked targets in the Gaza Strip overnight in response to rocket fire by Palestinian militants.