Hamas spokesman Fawzy Barhoum said in a statement Imad al-Alami, a former member of Hamas's highest political body, was wounded while "inspecting his personal weapon in his home and is in critical condition".
A medical source said he had been rushed to a hospital in Gaza City.
There was no independent confirmation of details of the incident.
Alami has for decades been a senior member of Hamas, which runs the Gaza Strip.
He lived in exile for more than 20 years but returned to Gaza in 2012.
His home in Gaza was bombed by Israel during the most recent war between the two sides in 2014.
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