Gunfire was heard on Friday morning at the wall - one of Judaism's holiest sites where hundreds of worshippers were attending prayers at the time.
Police say the guard shot the man after hearing him shout "Allahu Akbar".
The area, which is patrolled by armed guards, closed to visitors for about an hour but has now reopened.
The incident took place at about 07:40 local time (04:40 GMT) as the man emerged from a public toilet at the wall compound.
The man had his hands in his pockets at the time he was approached by the guard, the spokesman, Micky Rosenfeld, said.
The Western Wall is part of the Temple Mount (known to Muslims as Haram al-Sharif). It is venerated by Jews as a remnant from the complex which housed the Jewish temple until 70AD.
Jews go to the Western Wall to pray and leave prayers on pieces of paper between its ancient stones.
The site and the area around it has in the past been a flashpoint for violence between Israelis and Palestinians.
If an Israeli soldier shot another Israeli Jew because his saying "Allahu Akbar" instantly qualified him as a Palestinian militant, clearly their definition of "militant" is quite loose.
But, then again, Muslim extremists and terrorists do indeed tend to yell "Allahu Akbar" before detonating themselves in the middle of innocent people. This is a sad fact.
My question simply is, why on earth did the Israeli man yell "Allahu Akbar"?