The attacks on Tuesday targeted three locations in Gaza, officials told Al Jazeera.
The Israeli military said it carried out the air attacks in response to a rocket fired towards Israel.
Hamas spokesman, Hazem Qasem, rejected Israel's claims.
"The airstrikes targeted Hamas positions in the centre of the Gaza Strip," Qasem told Al Jazeera.
"The occupation claims that a group from Gaza launched rockets at them, but there is no side in Gaza that has claimed responsibility.
"We are maintaining the period of calm and did not launch any rockets. It is not beneficial for the occupation to violate this period of calm."
The emergency director at the al-Shifa hospital in Gaza, Ayman al Sahbani, told Al Jazeera that three of the injured were discharged after undergoing treatment.
"The fourth person, a 26-year-old, is in serious condition. He has a fractured skull and is unconscious in the ICU," Sahbani said.
Israel holds Hamas responsible for all fire coming out of the Gaza Strip.
For the last decade, Hamas has been the de facto government of Gaza, while the Fatah-led Palestinian Authority has controlled the West Bank.
Israel and Hamas have fought three wars since the group took control of Gaza, most recently in 2014.
Source: Al Jazeera and news agencies