One of the dead, Isa Saad Muhammad bin Awshan, was on the Saudi list of "wanted militants".
In a statement broadcast on Saudi al-Ikhbariya television on Wednesday, the Interior Ministry said Johnson's head was found in a freezer in an apartment - one of three locations searched following Tuesday's raid.
The rest of the body has not been found, the ministry said.
The US Embassy in Riyadh issued a statement saying the Saudi authorities had informed it they had found "what they believe to be the head of Paul Johnson".
The embassy's consular section was in the process of notifying Johnson's family in order to identify the head, the statement said.
Saudi forces inspecting cars at a
random security check in Riyadh
Earlier, an Interior Ministry official said Saudi authorities were holding the wife and three children of Salih Muhammad al-Awfi, the man believed to be al-Muqrin's successor, after the raid in which two anti-government fighters were killed and three security personnel were wounded.
A pan-Arab news station reported that al-Awfi might be among the casualties.
An Interior Ministry official said a gun battle erupted when a security team came under heavy fire while inspecting a residence suspected of being used by Saudi dissidents.
Just last week, US authorities announced the search had been called off for the body of the Lockheed Martin engineer who worked on Apache helicopters.
Johnson, 49, had been in the kingdom for over a decade when he was kidnapped on 12 June in Riyadh by captors who followed through on a threat to kill him if the authorities did not release its al-Qaida prisoners.
An al-Qaida-linked group claiming responsibility posted an internet message on 17 June that showed photographs of a decapitated body. Later a video of the beheading was posted on the same website.
Hours after the pictures of the beheading appeared on the internet, Saudi security forces shot and killed Abd al-Aziz Al-Muqrin, the alleged mastermind of Johnson's capture and execution.