Saudi-owned television later showed the prince, apparently suffering from minor injuries, meeting King Abdullah to explain what happened.
"This will only increase our determination to eradicate this (militancy)," Prince Muhammed said.
The prince, a top security official involved in the kingdom's aggressive anti-terrorism campaign, has been largely credited with the government's recent success in halting the violence.
Hussein Shobokshi, a columnist for the London-based Asharq Alawsat Arabic newspaper, told Al Jazeera the attempt on the minister's life had taken the "war on terror" to another level.
"It has also created an incredible amount of sympathy for the government," he said, adding that the the response [from the government] will be "strong, consistent and with enormous popular backing".
Shobokshi said the attack could be linked to the arrest three weeks ago of 44 members of al-Qaeda.
The authorities also seized large amounts of weapons and explosives during the raid, the Saudi interior ministry said.
The attack on Muhammed bin Nayef is the first known assassination attempt against a member of the royal family since the government began its crackdown on al-Qaeda-linked groups eight years ago.