Islamic State, which operates sleeper cells in lands it once ruled, claimed responsibility for the attack in a statement on its Telegram channel.
Abu Hussein al-Husseini al-Quraishi took over in November 2022 after his predecessor was killed, also in Syria.
The four dead included a police colonel, officials said. Six people were also wounded.
Islamic State on Monday claimed responsibility for the suicide bombing of a political rally in Pakistan that killed at least 45 people.
Once Britain's most high-profile Islamist preacher, Choudary has been charged with three terrorism offenses after being arrested in London last week.
The Iraqi prime minister began an official visit to Syria on Sunday, for the first time since the outbreak of the Syrian war.
The suspects arrested in Germany had also been collecting money for Islamic State since April 2022 and repeatedly transferred it to the group abroad.
Although Iraq’s last election in October 2021 gave a majority of seats to the main anti-Iranian political bloc, that of Shia Muslim cleric Moqtada al-Sadr, it did not give him victory.
Islamic State's Libyan branch was one of the militant group's strongest outside its original territory in Iraq and Syria, taking advantage of the chaos and warfare.
IS selected al-Qurashi as its leader in November 2022 after the previous IS leader was killed in an operation in southern Syria.