AU Peace and Security Commissioner Said Djinnit told reporters that the mission could be jeopardised without more resources from the international community.
"As of today we have only resources in cash to maintain the mission to the end of March [2006 or] very early April," he said at the AU headquarters in the Ethiopian capital, Addis Ababa.
His warning came despite the European Union providing 70 million euros [US $84 million] to the AU on Friday to help cover a shortfall of around $135 million.
"We are concerned about this because we have to maintain the mission and you have to have resources if you want to maintain the mission," he added.
However, Djinnit stressed that the AU had no plans to pull out of Darfur, even with cash shortfalls.
He said the mission had struggled to get funding from the international community since its inception despite a pledging conference in Addis Ababa earlier this year.
Currently the AU has 6,932 staff in Darfur, 5,623 military observers and 1,309 civilian police.
Analysts have credited AMIS - which has been in Darfur since 2004 - with helping calm the situation in some areas of strife-torn Darfur.
An AU-led assessment mission to Darfur concluded on Thursday that the presence of AMIS had contributed to reducing the number of ceasefire violations and afforded some level of protection for the delivery of humanitarian assistance.
"The AU force has helped to establish more stability. They have done an admirable job, highly professional, with much dedication," Jan Pronk, the Special Representative of the UN Secretary General for Sudan, told the UN Security Council in July.
Djinnit said he hoped to secure finances by January, when "important decisions should be taken in terms of providing resources to enable the mission to be maintained for the agreed timeframe or in terms of discussing other options."
The Darfur conflict erupted in February 2003 when the rebels took up arms to fight "discrimination and oppression" by the Sudanese government. The government is accused of unleashing militia on civilians in an attempt to quash the rebellion. Some 3.4 million people have been affected by the conflict.