The two organisations said they were retained in early July by al-Awlaki's father, Nasser, to bring a lawsuit over the alleged kill order.
But they said the US decision prohibits them from providing legal counsel to Nasser without permission because it would benefit his son, who has been named a "specially designated global terrorist" by the US treasury department, outlawing any dealings with him.
The petition filed in federal court in Washington alleged that the US treasury has refused to grant a license that would allow the groups to file a lawsuit challenging the government's use of lethal force.
The US added al-Awlaki to its terrorism blacklist earlier this year, targeting him with sanctions aimed at cutting off his financial support.
Al-Awlaki, now based in Yemen, rose to prominence last year after it emerged that he had communicated by email with Major Nidal Hasan, a US army psychiatrist accused of opening fire on colleagues at Fort Hood, Texas, killing 13 people.
Al-Awlaki has also been linked to Umar Farouk Abdulmutallab, a Nigerian student accused of trying to blow up a Detroit-bound flight with explosives in his underwear on December 25.
According to a treasury department statement, al-Awlaki is a key leader of al-Qaeda in the Arabian Peninsula (AQAP), has pledged an oath of allegiance to its emir, Nasir al-Wuhayshi, and "plays a major role in setting the strategic direction for AQAP".
Al-Awlaki was imprisoned in Yemen in 2006 on charges of kidnapping for ransom and being involved in an al-Qaeda plot to kidnap a US official but was released from jail in December 2007 and subsequently went into hiding in Yemen, according to the treasury department.
A US official said in April that the Obama administration had authorised the killing of al-Awlaki, after US intelligence agencies concluded the cleric was directly involved in anti-US plots.
But the White House pushed back strongly against the accusations that the government was trampling on civil liberties on Tuesday.
"Let's be clear about Anwar al-Awlaki," Robert Gibbs, a White House spokesman, said.
Awlaki "is someone who has sworn allegiance to Al-Qaeda in the Arabian Peninsula, is a regional commander for that group in Yemen, has and continues to direct attacks there and, as we know, against innocent men, women and children in this country," he told reporters.
"And this president will take the steps necessary to keep our country safe from thugs like him."