Do Prado was charged with driving under the influence after being stopped by police on Bank Holiday Monday, before being bailed to appear in court on Wednesday, September 12.
Saints boss 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.
"When I make a decision what to do about it, the news will come out. In the meantime, we will deal with it privately."
Adkins did not reveal whether Do Prado will be included in his squad to play Manchester United this weekend.