Security was already heightened during the Hajj season due to sectarian strife between Sunni and Shia Muslims in Iraq.
Saddam, a Sunni, was admired by many for standing up to the US. Hajj authorities fear that his death could stoke tensions between Sunni and Shia pilgrims.
"This is unbelievable. Things will not improve in Iraq now that Saddam is dead," a Syrian pilgrim said.
"They are American collaborators, those in Iraq. They should be executed, not Saddam Hussein"
"There will be more violence and more Arab anger towards the West."
For some Iraqi Kurds, the execution was a "fair decision" regardless of timing, though it has dashed hopes of justice for crimes against them.
Saddam was due to face charges against Iraqi Kurds during a second trial in what is known as the Anfal, or "spoils of war", campaign. This was due to resume next month.
Angered by Saddam's execution, many Arabs have said that the Iraqi government, which backed the US invasion in 2003, should have been tried, not Saddam.
"They are American collaborators, those in Iraq. They should be executed, not Saddam Hussein," a Lebanese pilgrim said.
"Saddam Hussein is the most honourable of all of them. He is the most honourable Arab. They will go to hell, he will go to heaven."