"It is of course totally unacceptable for FIFA that a fan finds his way up to the dressing rooms of any participating team at any FIFA competition," FIFA spokesman Nicolas Maingot told reporters on Saturday.
"Security will be tightened so this never happens again."
Provincial police spokesman Colonel Billy Jones said on Saturday that the man was first apprehended by FIFA officials.
"The man did not engage with any of the players," he said.
However, he was not then handed over to police after Friday's game but allowed to slip away into the crowd, he said.
Police have taken over security at Cape Town's Green Point stadium following a wage dispute between stewards and the contracted security firm.
"The man was wearing a red t-shirt and jeans. We believe he is still in Cape Town," Colonel Jones said, adding he could face charges of trespassing.
Last night England spokesman Mark Whittle said the fan was apprehended and ejected by England's security forces.
"We reported the incident to FIFA. That is all there is to it," said Whittle, who added that the fan was on his own.
The South African Organising Committee has insisted that security at all the matches would be top-notch despite strikes from private security companies which forced the police to take over.
Many England fans were clearly disappointed with their team's display in the draw that dented their hopes of securing a place in the second round and they roundly booed their team off the field.
England, who drew their opening game with the United States 1-1, need to win their final group game against leaders Slovenia to make sure of going through to the last 16.
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