Is this sentence grammatically correct? and can you tell me another good expression?
'I'm afraid my having updated the schedule on Google Calendar led to that message by mistake.'
(I said this when Google Calendar automatically sent the message about declination to the meeting host by mistake.)

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I would suggest:

I'm afraid that when I updated my schedule on Google Calendar it caused that message to be sent by mistake.

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The only real problem I see with your sentence is that "led to" needs to be followed by an action. Instead, in your sentence it is followed by a noun. Notice how JK fixed that problem. Instead of saying "caused that message", he says "caused that message to be sent", which is an action.

Although "my having updated the schedule" is cumbersome, it is not wrong. It would be simpler to say
"By updating the schedule on my calendar, I'm afraid I triggered Google to send you that message in error".

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Thank you very much!