Care was arrested and subsequently cautioned after being caught urinating against a wall in Leeds in the early hours of Sunday morning.
It is Care's third alcohol-related incident in the last three months - with the 25-year-old dropped from the England squad by caretaker coach Stuart Lancaster after his previous misdemeanours.
However Harlequins director of rugby Conor O'Shea, who met with Care on Monday, will not be taking matters further.
O'Shea said: "After last Friday evening's match at Newcastle, our players were given a week off and Danny went to spend a few days with his parents at their home in Leeds.
"On Saturday evening, he went out with some friends in the city and took a taxi home. He was caught short and stopped the taxi to relieve himself.
"The situation Danny finds himself in is unfortunate and is one that could and should have been avoided. We have no intention of doing anything other than supporting Danny and continuing to work with him so he understands his position and the decisions he makes."
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