The attack took place just after 3am, while Pakistani and Afghan drivers waiting to deliver fuel to the US base at Kandahar airport were sleeping, said General Muslim Ahmed, the local Afghan military commander. No American soldiers were injured.
One of the injured drivers, Sher Alam, told The Associated Press he was woken by the initial blast and ran for his life.
"I was sleeping at the time and suddenly I heard an explosion. When I woke up there was a huge fire engulfing the fuel tanker near mine. We all ran away and there were more explosions," said Alam, whose feet and hands were injured by flying debris.
Tight security measures mean long waits for drivers delivering fuel to US bases in Afghanistan. Alam said he had been sleeping in his truck for 10 days waiting his turn to enter the base.
Ahmed said American troops arrived shortly after the blasts to put out the fire. No arrests were made, but suspicion fell on the insurgents.
"The Taliban perpetrated this terrorist activity," the general said.
By midmorning on Sunday, black smoke still billowed from the charred hulls of the tankers.
Taliban rebels have kept up attacks, particularly in the south, but have failed to launch any major uprising in recent months.
On Saturday, the top US general in the country predicted they might try to pull off a "high-visibility attack" in an effort to reverse their waning fortunes.
Lieutenant General David Barno said the future was against them and predicted the insurgency would be nearly destroyed within 12 months.