The London Evening Standard says a heated exchange threatened to boil over at St. Mary's last weekend.
With the score still goalless Chamakh bore down on Artur Boruc's goal but appeared to dive when the goal was at his mercy.
Referee Martin Atkinson promptly booked the Moroccan before Moxey initiated a war of words with his teammate that continued into the dressing room at half-time.
Palace boss Ian Holloway said: "I don't think I can repeat what I said at half-time, but I nearly took my jacket off to both of them.
"You have to deal with things. I've since called them in and showed them the incident and asked what it was about. It was amicable in the end but passions flare up when you are not winning.
"The passion was there and I think it shook everybody. It rocked this club, we are built on that togetherness."
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