The attack is likely to further increase tensions between Hamas -- which denied any involvement -- and president Mahmud Abbas's Fatah, with a reconciliation agreement between the two all but dead.
Palestinian intelligence chief Majid Faraj was also in the convoy but was not injured in the explosion, which occurred shortly after they entered the territory.
At least six people were wounded, with none of their injuries believed to be life-threatenin.
A security source in Gaza said the convoy was also fired on by unknown gunmen at the time of the explosion, before Hamas security forces sealed off the area.
After the attack, Hamdallah briefly appeared at the opening of a wastewater treatment facility in Gaza before cutting short his visit and returning to the Israeli-occupied West Bank, where his government is based.
"It was a very well-planned attempt. It was a roadside bomb about two metres into the ground," Hamdallah said at his office upon his return.
A statement on official Palestinian media said Abbas considered it a "cowardly targeting" of Hamdallah's convoy and held Hamas responsible.
There was no immediate claim of responsibility.