Iranian state media did not immediately acknowledge the attack in Koya, some 300 kilometers (185 miles) north of Baghdad.
The Rudaw satellite news channel aired video showing smoke rising from the base in Koya. It quoted a health official for the casualty count.
The secretary-general of the separatist group, Mustafa Mawludi, and his predecessor, Khalid Azizi, were injured in the attack, Rudaw reported.
Kurds represent about 10 percent of Iran's population of 80 million people, with many living in the mountainous northwest that borders Iraq and Turkey.
A string of recent attacks by the Democratic Party of Iranian Kurdistan, PDKI, mark the end of a 20-year cease-fire between its fighters and Iran, though Kurdish separatists have agitated for freedom for decades in the country's northwest.
The area had been largely quiet since the 1990s under the cease-fire. But Kurdish resentments grew recently. In one incident, the death of a Kurdish maid at a hotel in the northwestern city of Mahabad in May 2015 sparked unrest by local Kurds as opposition groups alleged Iranian security forces somehow had a hand in it.
Since 2016, clashes have erupted between Kurdish fighters and Iranian security forces, including the elite Revolutionary Guard, leading to casualties on both sides. The PDKI, operating out of the northern Iraq, claimed many of those attacks, which saw Iranian forces shell Kurdish positions just across the Iraqi border in response.