Do Prado, 30, was charged with driving under the influence of alcohol after being pulled over by police on Bank Holiday Monday before being bailed to appear at Southampton Magistrates' Court on September 12.
The Brazilian, who has been with Saints for two years and last month signed a one-year contract extension until 2014, has already issued a public apology. Adkins told BBC Radio Solent: "We take this matter seriously and we will deal with it in-house. I've got one rule and people face the consequences of their actions if they step out of line."
Do Prado was arrested after his black Porsche Panamera was seen being driven erratically along Southampton High Street in the early hours of Monday.
"The police have been involved in the situation I'm led to believe," Adkins added, refusing to confirmed if Do Prado would be axed for Sunday's Barclays Premier League clash with Manchester United.
"I'm not happy with it, but we will deal with it and we will get on with it.
"When I make a decision what to do about it, the news will come out. In the meantime, we will deal with it privately."
Following his arrest and charge, Guly issued a statement via Twitter.
"I wanted to apologise about what happened, especially for the club and the supporters of Southampton," he wrote.
"We players are very exposed and we have to be more careful in this kind of situation, controlling every step when we enter public life."