It did not immediately give details of the source of the explosion, in central Gaza.
"Tawfiq Abu Naim, director general of the internal security forces, survived a failed assassination attempt Friday after his car was blown up in the Nusseirat refugee camp," a ministry statement said.
"He was moderately wounded and was treated in hospital," it added. "The security services immediately began investigations to discover the circumstances of the incident and to catch the perpetrators."
The rival Palestinian movements signed a landmark unity deal this month aimed at ending their decade-long split.
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The PA is due to resume control of the Gaza Strip by December 1 under the deal.
However, previous such attempts at reconciliation have repeatedly failed.
A major sticking point is expected to be Hamas's refusal to disarm its 25,000-strong armed wing.
Hamas seized Gaza in 2007 in a near civil war with Fatah that followed an electoral dispute after polls won by the Islamist movement.
Hamas has faced increasing isolation and deteriorating humanitarian conditions in the Gaza Strip in recent months, including a severe electricity shortage.