The Willesborough Wyevale site, just off the A20 opposite the Pilgrims Hospice in Ashford, will shut on Sunday.
Firm bosses say they have been unable to find a suitable new home for their business, meaning staff at the centre could be out of a job.
Spokesman Sarah MacRory said: “We have evaluated alternative locations for our business but have found nothing suitable.
“There are 12 people currently employed by Wyevale at the Ashford garden centre, and we have entered into a consultation period with the impacted colleagues and hope to find suitable alternative employment in nearby centres for as many as possible.
“It is not possible to say how many of these will be redeployed to other centres until the process is finished but we are doing our utmost to retain as many colleagues within the business as possible.”
Wyevale bosses say their Hamstreet centre, in Marsh Road just outside the village, will remain open.
Construction of the multimillion-pound junction is expected to start in the new year before opening in summer 2019.
Transport secretary Chris Grayling gave the project – which will be built 700 yards east of the current junction – the green light last month.