Johnson is understood to have urinated outside a St Kilda Road police complex in the early hours of the morning.
As a result of his actions, Johnson remains captain of Richmond but volunteers to sit out the upcoming match against North Melbourne in Round 2.
"I deeply regret my actions, I'm disappointed that I've let the club, our supporters and my teammates down," Johnson said in a statement.
"As captain, I have preached a message that I've failed to uphold.
"Fronting my teammates at the next training session will be the most difficult time I face in football.
"I take full responsibility for my behaviour and accept the penalty that the club has imposed."
