You can do this both at the property level and the per night level.
Note: Booking.com doesn’t allow specific granularity on check-in and check-out dates, and the check-in/check-out restrictions covered in this article are not applied for Booking.com channel.
You may need to block the date off completely, which will work for both check-in and check-out restrictions for Booking.com.
On the main settings tab of the property, there is a field for Only Check In on and a drop down to select the days of the week you wish to allow check-in. It defaults to no restrictions, but if you want to restrict some night, you can check the nights you do want to allow check-in.
There is not currently a field for Only Check Out on. You will need to do this at the per night level.
Per Night level:
Within the pricing tab of the property you can click on a date and the Set Your Daily Rate pop up will appear. You can check boxes to prevent check in or check out on that specific day.
If there is already a booking in place, on the Pricing tab, you will notice on the check-out date of that booking, the UI will be as below:
As there is already a check-out on that date, it will prevent an extra checkout.
In case you want to change the check-out date of the current booking, you can just edit the booking accordingly to reflect the change.
For more details, please refer to this help article Modifying a Reservation.