Several vehicles belonging to US-led forces were torched or otherwise damaged, and three alleged attackers were killed but the main section of the base was not breached.
The Taliban claimed responsibility for the strike in the Torkham area, the latest in a surge of attacks in Afghanistan as US-led foreign troops reduce their presence ahead of a full withdrawal by the end of next year.
Nato confirmed there had been a series of explosions in the area but said none of its personnel was killed.
No members of the Afghan security forces or civilians were killed or wounded, according to Esa Khan Zwak, chief administrator in Mohmandara district, in which the base is located.
Ahmad Zia Abdulzai, spokesman for the governor of Nangarhar province, said several militants wearing suicide vests and carrying other weapons staged the attack, and that Afghan and US forces exchanged gunfire with the insurgents.
Nato helicopters joined the fight, he added.
The encounter lasted three and a half hours, said Masoum Khan Hashimi, the deputy provincial police chief in Nangarhar province.
Afghan security forces trying to clear the area had to defuse a bomb in a car, although at least one car bomb was also successfully detonated in the attack, Mr Hashimi said.
Militants on both sides of the Afghan border have frequently targeted Nato supply lines.