Yes, a Muslim can also be jealous since he is also a human though he should not nourish the sentiments of jealousy. I mean these sentiments may go through him like a sudden violent wave of emotions but he ought to eliminate these as soon as he becomes aware. A task no doubt difficult yet essentially to be done.

All we know about jealousy is that it is not a desirable state of mind; it is sinful and profane thinking. We however cannot pronounce judgment about the jealous person. Why should we? We have no idea of the influences such people must have gone through; their intellectual capacity; the upbringing they received and their cultural background et cetera. We should never pass judgment against anyone. Leave that we must to God alone.

The Holy Qur'an reads:

O Prophet! Why bannest thou that which Allah hath made lawful for thee, seeking to please thy wives? And Allah is Forgiving, Merciful. Allah hath made lawful for you (Muslims) absolution from your oaths (of such a kind), and Allah is your Protector. He is the Knower, the Wise. (66:1-2)

When the Prophet confided a fact unto one of his wives and when she afterward divulged it and Allah apprised him thereof, he made known (to her) part thereof and passed over part. And when he told it her she said: Who hath told thee? He said: The Knower, the Aware hath told me. (66:3)

These verses allude to two events. Allah has admonished the Prophet (pbuh) and His wives in these verses; and also exhorted them to the right approach in the affairs at hand. But the true nature of events have not been unfolded neither here nor anywhere else in the Holy Qur'an. Why not just pick the lesson and leave the details the authenticity of which cannot be substantiated beyond any shadow of doubt.

The lesson is:

1. There is no reason to drag anything in the ambit of forbidden things which Allah has allowed even to please your dear ones. In other words, a person should decide matters in the religious affairs keeping aside affinities and associations.

2. A wife should not disclose her husband's secrets to anyone. Generally speaking, secrets of all those who confide in us should be preserved. We should never break their trust.