Imad al-Alami, a former member of Hamas's highest political body and its ambassador to Iran, died overnight, a Hamas statement said.
His funeral will take place in Gaza today, with large crowds expected.
Alami was wounded on January 9 while "inspecting his personal weapon in his home" in Gaza, Hamas said at the time.
There was no independent confirmation of the circumstances of the incident.
Alami had been a senior member of Hamas, which runs the Gaza Strip, for decades.
More From This Section
In 2003 while believed to be based in the Syrian capital Damascus, the United States labelled him a "specially designated global terrorist."
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.