Britain's Press Association said the pair were disciplined after returning drunk from a night out on Sunday during a three-day get-together in Teddington, southwest London.
Leicester centre Tuilagi has 26 global caps but has not played for England this year due to a knee injury, although he was expected to feature in coach Eddie Jones' plans for the forthcoming matches.
We look at his misdemeanours... In 2010, he was nearly deported by the Home Office after it emerged he had been living in the United Kingdom for six years on an expired visa.
The then 19-year-old had originally entered the country on a holiday visa six years earlier and had stayed on illegally.
After the successful appeal he was granted indefinite leave to remain.
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He had originally been banned for 10 weeks but that was reduced in light of a push by Ashton.
"We are at an incredibly important stage with two years to go to the Rugby World Cup in Japan and there is still a big step to make if we want to be the number one team in the world", Jones said.
Tuilagi also wore the gumshield in the victory against Argentina and the Rugby Football Union described the breach as a "genuine error". "He was a player that demolished New Zealand [in 2012] and we need those kind of players", said Jones of Tuilagi on Friday.
New Zealand-born Sale wing Solomona, 23, made his England bow during a two-Test tour of Argentina in June, crowning his debut with a match-winning try in a 38-34 win in San Juan.
In September 2013, Tuilagi issued an apology to Prime Minister David Cameron after he made a "bunny ears" sign behind his back during a photograph taken outside 10 Downing Street. And he missed the 2015 World Cup after an incident in Leicester in which a taxi driver and a female police officer were allegedly assaulted.