Palestinian security officials said that Rifaat Kulab, commander of the preventive security agency in the southern town of Khan Yunus, was shot seven times on Wednesday.
They described his condition as moderate and his life as not in danger.
A Hamas activist was shot dead outside his home after the attack.
Hamas members accused the security agency of shooting the man, and later set the commander's home on fire.
Security officials said the commander's mother and family were in the building.
Tensions between Abbas's Fatah movement and the ruling Hamas group have been rising since Hamas won legislative elections in January and ended Fatah's 40-year hold on the Palestinian leadership.
Fatah and Hamas are in a battle over control of the security forces, leading to factional fighting in Gaza's streets.
A Hamas attack on a security office in Gaza on Monday led to a day-long gun battle in the southern town of Rafah, and caused a rampage by Fatah security men against government buildings in the West Bank later in the day.