The attacks struck training grounds used by Palestinian militants, leaving two people lightly injured, they told AFP.
The Israeli military confirmed a series of overnight strikes in a statement which said it had struck five rocket-launching sites in northern Gaza, as well two other sites in central and southern areas of the strip.
The raids took place after militants fired five rockets at southern Israel, one of which hit an open area. Two were intercepted by the Iron Dome anti-missile system while the other two landed inside Gaza, the statement said.
She was one of four people wounded in the incident, they said.
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There has been a noticeable uptick in Palestinian rocket fire at Israel in recent weeks, leading to a series of almost nightly air strikes by Israel.
The increase in rocket fire comes as Israeli troops stage a wide-ranging manhunt for three teenagers who disappeared from the southern West Bank on June 12, with the Israeli government blaming militants from the Islamist Hamas movement.
Since the beginning of the year, Gaza militants have fired more than 200 rockets at southern Israel, army statistics show.