Their son Prince George was reportedly "very polite" when he chose a fruit juice from the garden centre's cafe this week.
The royals live nearby at Amner Hall.
Staff at the centre have been told not to comment, after the visit to the centre became big news in royak-watching magazines such as Hello!
The garden centre was built in 1985 and extended in 2008. The pets and aquatics centre was refitted this year.