The men were carried off into a car as they left a mosque at dawn after morning prayers in the town of Khan Yunus, officials and witnesses said on Wednesday.
They were then beaten and shot in the legs before being dumped at a petrol station. One of the injured men later died in hospital, medical sources said.
Although no one has claimed responsibility for the incident, one Hamas official blamed rival Fatah gunmen loyal to Mahmoud Abbas, the Palestinian president.
The two sides have been engaged in a power struggle since Hamas won elections in the Palestinian territories earlier this year.
Clashes have intensified between Hamas and Fatah supporters since the Islamist-led government deployed a new 3,000-member paramilitary unit last week.
On Monday, the Palestinian prime minister, Ismail Haniya, urged both sides to show restraint, and pledged that there would be no civil war in the territories.