The video released on Monday did not show the face of the victim, however, and it was impossible to identify him conclusively.
In an earlier internet posting last week, the group had claimed to have killed Schulz, and then later said it would show the killing.
The victim was kneeling with his back to the camera, his hands tied behind his back, and blindfolded with an Arab headdress when he was shot. The video also showed Schulz's identity card.
Schulz, a civilian contractor, has been identified by the group as a security consultant for the Iraqi Housing Ministry, although neighbours and family from Alaska, where he lives, say he is an industrial electrician who has worked on contracts around the world.
Meanwhile, Susanne Osthoff, the German woman taken hostage in Iraq, has been freed, Germany's foreign minister said.
Osthoff was freed on Sunday
Frank-Walter Steinmeier said on Sunday: "I am glad to be able to announce to you ... that Mrs Susanne Osthoff is no longer in the hands of the kidnappers.
"As of today, she is in the safety of the German embassy in Baghdad. Our impression after talking to her is that she is in good physical condition."
Diplomats said that Shalid al-Shimani, her Iraqi driver, had also been released.
"I am glad to be able to announce to you ... that Mrs Susanne Osthoff is no longer in the hands of the kidnappers"
Frank-Walter Steinmeier, the German foreign minister
Osthoff, 43, a convert to Islam, has been living in Iraq for 10 years. She is married to an Iraqi who belongs to Shammar tribe, the largest Sunni tribe in central and northern Iraq.
She disappeared on 25 November in northern Iraq along with al-Shimani.
The German authorities did not identify her captors.