Mohammed Ebayat was speaking on a telephone near the Al Hussein Hospital when it exploded, killing him instantly.
Following the incident, the group, which is affiliated with Palestinian Authority Chairman Yasser Arafat's Fatah movement, accused Israel of assassinating Ebayat. The 27-year-old was a senior Al Aqsa activist in the Bethlehem area.
The organization described the death of Ebayat as "another Israeli crime," and vowed to retaliate for the killing.
The Israel Defense Forces refused to comment late Sunday on the explosion at the phone booth, but were preparing for possible retaliation against the town of Gilo from Beit Jalla.
The Al Aqsa Martyrs Brigades has been blamed for dozens of armed attacks and suicide bombings against Israeli interests in the West Bank and Gaza and in Israel proper.
Notable deaths of 2014 [PHOTOS]