First a small clarification from Wikipedia entry
Contrary to false impression generated in recent decades by Indian movies and TV soap opera, the practice does not exist in every part of India, nor is it an integral part of a marriage ceremony.
Apart from the mangala sutra, the toe rings (bichhua), kumkum, bangles, nalla pusalu (black pearls) and nose ring form six symbols that may indicate that a woman is married.
So when we say Mangal Sutra, we mean any of the above symbols that indicate marriage status.
Coming to the question, I think it has to do with prevalence of Polygyny. A man could have many wives, but not otherwise. So women would need an indication for their marital status, a "taken" tag if we may call it. Where as men don't need any.
As I said this is just my guess, have no references.
Mangala Sutra is integral part of Hindu Marriage.
This practice is an integral part of a marriage ceremony as prescribed by Manusmriti the traditional law governing Hindu marriage.
Polyandry also existed in Hinduism but it was less prevalent when compared to Polygyny.