I have seen people put a comma right after an em dash. Is this practice correct? I guess it is not, since the em dash takes the place of the comma.
Swan's PEU describes this. The em-dash does not take comma after it. That's because, as you said it correctly, it replaces a comma so you don't need to put it again.
An em-dash may replace commas, semicolons, colons, and parentheses to indicate added emphasis, an interruption, or an abrupt change of thought.
Grammarbook gives us an example of em-dash replacing comma:
You are the one, the only one, who offered to help me.
You are the friend—the only friend—who offered to help me.
Here are the other examples.
I need three items at the store—dog food, vegetarian chili, and cheddar cheese (colon)
I wish you would—oh, never mind (abrupt change)