"Two more cases died today, a 25-year-old woman and a 35-year-old man, bringing the total number of deaths from A(H1N1) to 10," said Hassan Khalaf, a ministry spokesman.
He added that another 67 people have been stricken with the disease, including "a number of serious cases."
Gaza, which has been under strict Israli closure since the Islamist Hamas movement seized power in June 2007, was among the last places in the world to see cases of the virus, the first of which were reported a week ago.
The ministry has demanded 300,000 vaccines for the impoverished territory of 1.5 million people, including some 13,000 vaccines for government and public and private health workers.
Israel has already allowed in 10,000 doses of swine flu vaccine in a bid to prevent the latest outbreak from spreading to the Jewish state, which has lost 67 people to the virus.
Israel said last week it will allow in 30,000 to 40,000 more vaccines supplied by the World Health Organisation, but the transfer has not yet taken place, according to a military spokeswoman.
The Hamas-run government has meanwhile started examining foreigners entering the territory through the Erez crossing with Israel for signs of the disease, including by taking their temperature.