Germany's Der Spiegal reported that a two star U.S. general was killed in the attack. ISAF declined to comment but said one of its service members had been killed in the attack that took place at around noon.
"The wounded German general, whose life is no longer in danger, is being given medical treatment," it said.
The Afghan president was quick to condemn the attack, saying the delegation had been visiting the facility to help build Afghanistan's security forces.
Afghanistan's Defense Ministry confirmed the gunman was wearing an Afghan army uniform.
"Today at 12pm, a terrorist in army uniform opened fire on international partners and other Afghan officers, wounding several," the statement said.
Such attacks have eroded trust between the allies and complicated efforts to train Afghanistan's 350,000-strong security force.
In a similar attack on Tuesday, several were wounded in eastern Paktia province when a policeman opened fire on international and Afghan forces, police chief Zalmay Oryakhil said.
The Taliban says insider attacks reflect their ability to infiltrate the enemy, while ISAF officials say the incidents often arise over misunderstandings or altercations between troops.
In 2012, dozens of incidents forced international troops to take measures to reduce interaction with their Afghan partners and since then, the number of insider attacks has fallen sharply.
Adding to the tension, a NATO airstrike hit a vehicle carrying civilians in western Herat province, local officials said, killing four members of one family including two children.
"We strongly condemn the killings by foreign troops and we have reported this to the presidential palace," deputy provincial governor, Aseeluddin Jameh, told Reuters.
"The family was coming back from a wedding in Shindand district when they were hit."
(Reporting by Jessica Donati, Hamid Shalizi and Krista Mahr in Kabul; Jalil Ahmad Rezaee in Herat; Ahmad Sultan in Gardez; Editing by Janet Lawrence)