Witnesses said protesters threw shoes and eggs at Awad's car as he entered Gaza through the Rafah border crossing.
Officials said he left the Palestinian territory shortly afterwards.
Protesters also gathered at Shifa hospital in Gaza City, carrying posters criticising Awad and the recently formed government of technocrats to which he belongs.
The government was sworn in on June 2 following a unity deal between the Islamist Hamas movement and president Mahmud Abbas which ended seven years of rival administrations in the West Bank and Gaza.
"We don't want this visit and all the Palestinian people are opposed to it and reject it," he told AFP.
Protesters said they were angry that it had taken Awad eight days to visit Gaza, where 193 people have been killed in Israeli air strikes.
They also condemned the Palestinian president for failing to do more to halt the Israeli campaign, with some chanting: "Abu Mazen (Abbas) is a collaborator."
In a statement, the health ministry condemned the "flagrant and brutal assault" on the minister and his delegation in Rafah, blaming the incident on "media affiliated with Hamas."
"The ministry of health will continue to stand by our people in Gaza," the statement said, pledging to secure medical supplies for the wounded.
There was no immediate comment from Hamas, but a top member of its exiled politburo, Mussa Abu Marzuq, condemned the incident as "irresponsible and improper" on his Facebook page.
He called for an investigation and prosecution of those responsible.
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