Prince Mohamed bin Nayef, who chairs the Saudi Hajj committee, ordered the probe during a meeting on Thursday with senior officials responsible for the pilgrimage in Mina, where the stampede took place.
The findings of the investigation will be submitted to King Salman, "who will take appropriate measures" in response, the Saudi Press agency said.
The Saudi Arabian interior ministry says the crush of Muslim pilgrims appears to have been caused by two waves of pilgrims meeting at an intersection.
A brief history of disasters at Mecca and Medina
Ministry spokesman Major General Mansour al-Turki said high temperatures and fatigue might also have been factors in the disaster, the deadliest event to afflict the Hajj pilgrimage in more than two decades.
However, the head of Iran's Hajj organisation, Said Ohadi, said that, for "unknown reasons," two paths had been closed off near the site of a symbolic stoning of the devil ritual where the stampede occurred.
"This caused this tragic incident," he said on state television, according to the Associated Press news agency.
Ohadi said the path closures had left only three routes to the area where the stoning ceremony was held.
Mina houses more than 160,000 tents where people spend the night during the pilgrimage.
Al Jazeera's Basma Atassi, reporting from Mina, said the incident took place in a street between pilgrim camps.
"The street where it happened is named Street 204. 
"During and after the stampede the pilgrims continued to flock into Mina to perform the devil stoning ritual."
Amateur video shared on social media showed a horrific scene, with scores of bodies - the men dressed in the simple terry cloth garments worn during Hajj - lying alongside crushed wheelchairs and water bottles.
The head of the Central Hajj Committee, Prince Khaled al-Faisal, blamed the stampede on "some pilgrims from African nationalities," Saudi-owned al-Arabiya TV channel reported.
Survivors assessed the scene by standing on the top of roadside stalls as rescue workers in orange and yellow vests combed the area.
About 4,000 people from rescue services were participating in the operation to help the injured and about 220 ambulances were directed to the scene, a civil defence spokesman said.
Deadly Hajj incidents
Saudi authorities take extensive precautions to ensure the security of the Hajj and the safety of pilgrims. But tragedies are not uncommon.
In 2006, more than 360 pilgrims were killed in a stampede, also in Mina.
The day before the 2006 Hajj began, an eight-storey building being used as a hostel near the Grand Mosque in Mecca collapsed, killing at least 73 people.
Two years earlier, a crush at Mina killed 244 and injured hundreds on the final day of the pilgrimage.
And, in 2001, a stampede at Mina killed 35 people.
The worst Hajj-related tragedy, which happened in 1990, killed 1,426 pilgrims in a stampede in an overcrowded pedestrian tunnel leading to holy sites in Mecca.
Source: Al Jazeera