In Massachusetts, the possible grounds for divorce are cruel and abusive treatment, utter desertion, adultery, intoxication, impotency, nonsupport, confinement to prison for 5 years or more, and irretrievable breakdown (i.e. the no-fault standard).
The possible grounds for annulment are incest, polygamy, being underage, being insane, failure to properly complete the marriage, impotence, fraud, misrepresentation of chastity, misrepresentation of disease, and duress.
If one party conceals that they have a sexually transmitted disease then that could be considered a fraud and sufficient to annul the marriage. If the parties lived together or consummated the marriage after this knowledge was learned that action would likely remove the misrepresentation as a basis for annulment.
If you are not able to obtain an annulment, you would still be able to obtain a divorce. It is possible you could argue for divorce based on impotence, which is strictly defined as an inability to have sexual intercourse. The existence of an STD could be argued as impotence although not technically making intercourse impossible. As with any fault argument, you would bear the burden of proving this fault as a prerequisite to obtaining the divorce, which is one of the reasons we often counsel clients not to file fault divorce cases (as discussed in this previous post: Is No-Fault Divorce a Good Thing? It may soon be the law in all 50 states.).
It would be easier, therefore, to simply apply for divorce based on the no-fault standard in which you could claim an irretrievable breakdown without having to prove the existence or impact of the STD.
For more information about Annulments read our previous post specifically on that subject: Can I obtain an Annulment?