Capital Gardens, which runs the centre, sold the freehold to the land on which it is located – known as Highgate Bowl – in September last year.
Capital Gardens managing director Colin Campbell-Preston said: "We have decided to close the garden centre and focus our efforts on our business in Alexandra Palace.
"We’re holding a closing down sale next Friday so will close once we’ve sold our stock."
He said sales at the Highgate site were down 34 per cent.
The site was bought for £2million by a company called Omved International Limited, based in the British Virgin Islands.
Campbell-Preston said two of the garden centre staff would take up new roles at Alexandra Palace, while three had decided to leave and others had taken redundancy.