Television footage showed some people were wounded in the clash.
Egypt opened the crossing for two days to allow in Palestinians who need medical treatment not available in Gaza, and for Palestinians to return home.
Hundreds of Palestinians had gathered on the Gaza side of the border crossing, hoping to leave the impoverished and heavily-sanctioned strip.
Al Jazeera's Ayman Moyheldin, reporting from the crossing, said: "They have been waiting all day [and] there has been growing frustration that the Egyptian authorities have not been letting in enough Palestinians."
The Rafah crossing - the main gateway for Gaza's 1.4 million people to travel abroad - opened on Tuesday for the first time since May.
It was supposed to be open until Thursday, but authorities closed the Egyptian side of the terminal following clash.
The Palestinian interior ministry in Gaza also ordered the crossing shut down, telling all Palestinians to leave the area.
Rafah has largely remained sealed after Hamas seized total control of Gaza, forcing out security forces loyal to Mahmoud Abbas, the Palestinian president, more than a year ago.
The closure has prevented people from travelling for medical care, studies and family visits.
In January, however, Hamas blew up the border wall between Egypt and Gaza, allowing thousands of people to move in and out of Egypt for nearly two weeks before it was resealed.