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
A major error in paying disability and sickness benefits to 75,000 people is to be put right - at a potential cost of up to £500 million.
A 24-year-old man suffered a deep cut to his ear after another passenger leaned over and bit it during a row.
Wintry feel to end the week