Cymdeithas yr Iaith said in a letter to the NBGW: "As a national institution that receives significant public funding and support from the local authority and central government it stands to reason that there should be full Welsh language services available.
The group have asked First Minister Carwyn Jones and Carmarthenshire Council "to hold the funding back until the Garden shows due respect to the Welsh language".
National Botanic Garden director Dr Rosie Plummer said: "The Garden, as an iconic organisation and environmental flagship for Wales, is very committed to its wide support for the culture, language, and heritage of Wales and makes substantial allocation of resources and effort to this.
"It is therefore enormously disappointing to be subject to such vigorous approaches that largely seem to overlook the very wide range of ways in which the Garden actively contributes to bringing the unique importance of Wales to everyone who visits. The Garden works hard to promote and develop its language resources to the more than two million visitors it has welcomed in just 15 years.
"All our press releases, brochures, published materials, and visitor signage is bilingual and we take a great pride in the way in which we present our information and learning, and encourage use of the language in a friendly and engaging way."