Two rockets hit base at the airport in the town of Kandahar on Friday evening.
The Taliban occasionally fires rockets into the sprawling base, home to 7,000 soldiers and civilian workers, but they usually explode harmlessly on open ground.
Friday's attack was the first time anyone had been hurt.
Major Marc Theriault, the Canadian military spokesman, said one of the two explosions "occurred in a common area and several people from various nations were wounded, among them two Canadian soldiers".
The US military said 10 people were hurt. Three people had been treated for injuries and released from hospital, six were in stable condition and one was in serious condition, it said.
The Taliban commander for southern Afghanistan, Mullah Dadullah, claimed responsibility.
"We fired several rockets at the air base and they hit their target," said Dadullah, speaking by telephone from an undisclosed location, adding: "We will carry out more such attacks."
Theriault said the attack was the seventh since he arrived at the base in February. In all, 22 rockets had been fired, he said.