The charity has already opened the car park at Nostell Priory, near Wakefield, for access to the parkland - but spaces sold out straight away.
Now Beningbrough Hall, near York, will re-open on a similar basis on June 3. Capacity is limited to enable social distancing, and all visitors, including National Trust members, must book tickets online in advance. Anyone without a ticket will be refused admission.
The house itself will not be open but the gardens, parkland and toilets will be accessible. The art gallery, play area, cafe and shop will remain closed.
The first tickets released for the re-opening week have already sold out but more will be made available on the National Trust website every Friday.
Beningbrough is a Georgian country house surrounded by woodland, parkland and a river. Award-winning designer Andy Sturgeon has overseen a recent rejuvenation of the gardens, which include walled areas and garden rooms.
Book tickets here.
RHS Harlow Carr gardens in Harrogate will also re-open on June on a ticketed basis and the Bolton Abbey estate in Wharfedale has already re-opened, again for ticket holders only.
English Heritage will re-open four priority sites in Yorkshire - Whitby Abbey, Scarborough Castle, Mount Grace Priory and Brodsworth Hall - in early July.
Dalby Forest in Ryedale is open but the cafe, bike hire centre, play area and Go Ape attraction remain shut.