All three attackers were shot dead by helicopter gunships during the assault on the base in Nangarhar province, but no member of the US-led NATO mission was killed.
"Our investigation shows some 41 vehicles - supply trucks and vehicles belonging to US forces - were destroyed in the attack," Nangarhar provincial spokesman Ahmad Zia Abdulzai said after the attack near the Torkham border crossing.
"Magnetic bombs were attached to some vehicles and detonated," he told a press conference.
"Three armed insurgents were killed by US helicopter gunships. Weapons, suicide vests and hand grenades were found afterwards."
A senior Afghan border police official also told AFP that 30 to 50 vehicles had been burnt.
Torkham is next to Pakistan's Khyber Pass and straddles a key NATO overland supply route into landlocked Afghanistan from the nearest sea port of Karachi.
"There were a series of explosions that occurred in the vicinity of a forward operating base in Nangarhar province," said a spokesman for the International Security Assistance Force (ISAF).
The military later described it as an "attempted but unsuccessful coordinated attack by enemy forces".
"There were three enemy forces killed during the attack. We can confirm that no ISAF personnel were killed as a result of this incident," it said in a statement.
An AFP photographer saw the bodies of three dead attackers wearing Afghan police uniforms.
NATO combat troops are gradually withdrawing from Afghanistan and are due to finish their mission by the end of 2014, after presidential elections next April.
Zabihullah Mujahid, a spokesman for the Taliban which is leading a 12-year insurgency against Western troops and the Afghan government, claimed responsibility for the attack in a statement sent to the media.
The Taliban have launched a spate of attacks across the country in recent days, with scores killed in suicide bombings, ambushes and rocket attacks. They also killed five aid workers in the west.
On Sunday the bullet-riddled bodies of seven civilians kidnapped one week earlier by the Taliban were found in Ghazni province just south of the capital.
Also on Sunday, Afghanistan's ambassador to Pakistan and potential candidate for next year's presidential election, Omar Daudzai, was appointed acting interior minister.
President Hamid Karzai, who has led Afghanistan since the 2001 US-led invasion removed the Taliban from power, is barred from standing for a third term.
Interior minister Mujtaba Patang was voted out by parliament in July over accusations that he had failed to thwart the threat from Taliban rebels.
Afghanistan's 350,000-strong security forces are suffering a steep rise in attacks as the NATO mission winds down, with police and army casualties said to have increased by 15-20 per cent since 2011.
The election to succeed Karzai is seen as the key test of whether 12 years of massive international military and aid intervention has been worthwhile.
Karzai recently named controversial former warlord Abdul Rab Rasul Sayyaf, 2009 runner-up Abdullah Abdullah and former finance minister Ashraf Ghani as possible candidates.
Other potential runners include foreign minister Zalmai Rassoul, Qayum Karzai, the president's brother, and former interior minister Ali Ahmad Jalali.
Karzai has pledged to ensure a smooth election, but international donors have expressed concern about whether the vote will produce a credible result after the 2009 poll was marred by massive fraud.