Air strikes hit around Gaza's derelict international airport near the southern city of Rafah and in nearby farming areas, without causing casualties, said the ministry, which is run by the Islamist Hamas movement.
Israel's army said it had hit five sites operated by Hamas.
"The (Israel armed forces) will continue to operate in order to protect the civilians of Israel from all Hamas terrorist threats above & beneath ground," spokesman Peter Lerner said on Twitter.
There were no reported injuries and no claims of responsibility for the mortar fire.
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Hamas and Islamic Jihad, another militant Palestinian group, released separate statements warning Israel against any escalation along the border.
"Hamas holds the Israeli occupation completely responsible for the escalation east of Gaza and the consequences of it," spokesman Sami Abu Zahri said.
"The movement calls on the concerned parties to shoulder their responsibility to stop this aggression and Israeli crimes."