I suppose you're talking about the expression used at the end of a communication "take care", rather than "take care of you". In Italian that would sound quite weird, but I saw the difference with my girlfriend (who's not Italian) when she kept saying "take care".
In Italian we say: "stammi bene".
If you say "take care of you" I suppose someone would say the subject is missing, probably... as in "I'll take care of you".
EDIT: beatrice76, I can tell you we use it too (I'm from Milan).
Another way to translate it might be: "Riguardati". In this case you really mean "Take good care of yourself", for instance if the person has a cold.
Otherwise "stammi bene" would be the corresponding form of "take care".
For formal relationships: "Stia bene" or "Si riguardi".