Hamdallah was not injured in the explosion, which occurred shortly after his convoy entered the territory run by Islamist movement Hamas, a security source in the convoy said.
Palestinian intelligence chief Majid Faraj was part of the convoy but was not hurt either, the security source said.
A statement on official Palestinian media said president Mahmud Abbas considered it a "cowardly targeting" of Hamdallah's convoy and held his rivals Hamas responsible.
There was no immediate claim of responsibility. Radical Islamists opposed to Hamas also operate within the Gaza Strip and have regularly been behind unrest there.
The Hamas interior ministry confirmed there had been an explosion and said security forces were investigating the incident.
The two major Palestinian factions signed a reconciliation agreement in October that was supposed to see the Islamists hand over power, but it has all but collapsed.
Hamdallah appeared on television shortly after the explosion as he opened a plant in the territory.
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