"The priority now is to expel and defeat militants and terrorists in the camp. Under the present circumstances, a military solution is necessary," minister Ali Haidar said in Damascus.
He made the comments after meeting Palestine Liberation Organisation official Ahmed Majdalani, who travelled from the West Bank for emergency talks on the situation in the embattled Yarmuk camp.
"It is not the state that has chosen this, but those who entered the camp," added Haidar, referring to fighters from the jihadist group.
"The Syrian state will decide whether the battle requires it," he said, when asked if Syrian soldiers would participate in any operation.
IS forces attacked Yarmuk on April 1, and have seized large swathes of the camp, executing Palestinian fighters who sought to resist.
The group's presence in Yarmuk has sparked international concern for the camp's remaining residents, who have endured repeated bombardment and a siege of more than 18 months by the army.
Once a thriving district that was home to some 160,000 Syrian and Palestinian residents, Yarmuk has been wracked by violence since late 2012.
The Syrian army imposed a tight siege on the camp that reportedly led to deaths because of shortages of food and medicines.
An agreement between rebels and the government, backed by Palestinian factions in the camp, was reached last year and led to an easing of the siege, although humanitarian access has remained limited.
Yarmuk's population had dwindled to around 18,000 before the IS attack. Some 2,500 of those managed to escape in the past week.
On Monday, the UN Security Council called for humanitarian access to the camp, and Palestinian officials have urged that its residents be protected.