There is "no suggestion that Mark Harper knowingly employed an illegal immigrant", Downing Street have said.
The Immigration Minister has announced his resigned over the issue.
Number 10 said David Cameron had "accepted his resignation with regret".
More top news
Warwickshire Police are currently dealing with an "ongoing incident" at Bermuda Park, Nuneaton.
The Labour leader has called the Norwich South MP's remark "completely unacceptable" and says Clive Lewis has personally apologised to him.
Jamie Harron, was arrested in July over the incident in which he said he put his hand on a man's hip to avoid spilling a drink in a bar.