Abd Allah, 45, who joined the channel shortly after its launch in 1996, was killed after his vehicle veered out of control and crashed into a tree.
A leading London-based academic, Dr Bashir Nafia, who was also in the car, was injured in the accident in the early hours of Sunday morning.
"We feel a great loss at Mahir's death," said Jihad Ballut, spokesman for Aljazeera.
"He has been an integral part of the Aljazeera team for many years. Our hearts go out to his family and loved ones."
Born in the West Bank city of Jenin, Abd Allah was a strident commentator in both the Arab and international media.
Abd Allah, who also held a degree in mechanical engineering, began his journalism career at the London-based Middle East Broadcasting Corporation (MBC). He also worked for several other Arab media, including the al-Hayat newspaper, also based in London.
Abd Allah is well-known for hosting the popular weekly Aljazeera talk show, al-Shariaa wa al-Hayat (Islamic jurisprudence and Life) which focuses on all aspects of Islam from the perspective of various Muslim scholars.
Abd Allah (R) hosted cleric Shaikh
Yusuf al-Qaradawi on his show
The most prominent participant in the show, which is aired live and includes phone-ins from viewers, is Egyptian-born scholar, Shaikh Yusuf al-Qaradawi.
As a correspondent covering the US-led invasion of Iraq, Abd Allah narrowly survived the US missile attack on the channel's Baghdad bureau in 2003, in which his fellow journalist Tariq Ayub was killed.
Abd Allah has participated in various media discussions in both the Arab and international media.
He is survived by his wife and three children.