Administrators are Stephen Goderski and Peter Martin at PKF Geoffrey Martin and Co in London.
The gardens are based near St Albans. RNRS is a membership organisation, with members drawn from professional and amateur gardeners and horticultural businesses in the UK and around the world.
The gardens were due to reopen for 2017 on 10 June.
Royal patronage commenced in 1901 with Queen Alexandra and continued through to the late Queen Mother.
The gardens were redesigned and replanted in 2007; previously the gardens were planted solely with rose varieties, but the refurbishment saw the installation of a large formal garden featuring approximately 15,000 roses alongside companion planting. The gardens celebrated their 50th anniversary in July 2013.
The £500,000 redesign of the 5ha garden was by Michael Balston and was opened by garden writer Peter Seabrook. It was built by Adam Frost Landscapes and planting designs were by society members including Peter Beales, Brigid Quest-Ritson and David Stevens.
Work was funded by selling half the original site to nearby project Butterfly World, which closed in 2015.
Latest accounts for the year to 31 December 2015 showed a deficit of £35,000.
Seabrook said the closure was "terribly sad".
Harkness Roses' Philip Harkness said: "It is sad news. It's difficult being a single species plant society now. The overheads to run the place were not matched by the income from membership."
Peter Beales Roses nursery manager Ian Limmer said: "We are all devastated to hear of the society's demise. It's a terrible shame. The gardens are a beautiful site and it is so sad to think they may not be available for the public to visit."