New commercial director Katharine Poulter is believed to have taken on the top job on an interim basis. Jill Easterbrook remains as Dobbies chairman.
A Dobbies statement read: "James has led Dobbies for 23 years and leaves the business in good shape thanks to his long experience on the board. We have a good platform to bring the brand to more customers, working with the core Tesco business."
Barnes, son of former owner David Barnes, led Dobbies through a management buyout in 1994 and to the stock market in 1997. He remained in charge even after Tesco beat Wyevale to buy the business in 2007.
Dobbies sales for the year to February rose 22 per cent to £136.4m. Profits were up to £10.5m from the previous year's £9.9m. The 33rd Dobbies to open was a combined Tesco-Dobbies store in King's Lynn last October.
Garden Centre Association chairman Peter Burks said: "They've not had a very good season, on the back of a not-very-good season last year, so the board could have thought it was time for a change."
Watering sales were up 400 per cent last week, with compost up 100 per cent, as many garden centres finally caught up with 2012's poor sales figures after a slow start to the season.