Abd Allah al-Rashoud was killed during US air strikes on Qaim near the Syrian border, said the statement signed by Abu Musab al-Zarqawi who heads a group in Iraq linked to the al-Qaida.
Al-Rashoud is also said to have been on a Saudi wanted list.
The authenticity of the web statement could not be verified.
The statement said al-Rashoud left Saudi Arabia six weeks ago to join fighters in Iraq against US forces and the US-backed Iraqi government.
"The enemies of God could not defeat the unit which Shaikh Abd Allah al-Rashoud was part of ... when the crusaders failed to enter the area, they bombed the mujahidin with warplanes," it said.
US forces had recently launched a major offensive in Iraq, targeting al-Qaim near the Syrian border.