Tuilagi jested while standing next to Cameron on Monday. Members of the Lions were invited at the official residence of the prime minister following their 2-1 series victory over Australia this summer.
The centre took to Twitter to apologize, writing: "Apologies for messing around on Lions photo. No offence intended. Great Day at Downing Street. Thanks to Prime Minister for hosting us."
Tuilagi sparked controversy two years ago at the World Cup in New Zealand when he was fined 3,000 pounds by the English Rugby Union and cautioned by police after jumping from a ferry the day after England was eliminated by France in the quarterfinals.
The chief executive of the Rugby Football Union, Ian Ritchie, criticized Tuilagi's gesture and said England head coach Stuart Lancaster would "have some words" with him.
"Recognize it for what it is, not a good thing to do, apologize for it and then we need to make sure that those sort of things don't occur again," he told Sky Sports News.
Tuilagi's coach at Leicester Tigers, Richard Cockerill, told the BBC that the England centre would also write a letter to Cameron in addition to his message on Twitter.
"He has been a bit daft," Cockerill said. "He has made an error of judgment. He should know better. He is old enough and wise enough to know he shouldn't have done it. We have reminded him of his responsibility and he has apologized on Twitter and he is writing to the Prime Minister to apologize if there was any offence taken."