Wakefield Council said Rishworth Street would be closed all day for the demolition.
Northgate will close temporarily but is expected to reopen later that day.
People are being asked not to approach the safety cordon around the demolition, which will not be visible to watch.
Footage of the knock-down will be posted on our website.
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The ageing 1970s car park has been closed since the middle of July after council bosses decided to knock it down.
It will be replaced with a surface-level car park.