26 November 2015 Last updated at 13:08 GMT
The first virtual visitors were young patients at nearby King's College Hospital.
The small gallery attracts 160,000 visitors a year and has one of the finest collections of old masters in the UK, including paintings by Rembrandt, Gainsborough and Canaletto.
Now it has collaborated with Google to create a virtual tour using the Google Cardboard VR headset.
At King's College Hospital a group of six children tried out the app at the hospital's school room, where long-term young patients have classes.
They were able to look at pictures and wander through the gallery designed by Sir John Soane in the early 19th century.
The young visitors were mostly enthusiastic about the experience, though several said it could not match up to a real visit to the gallery, and one said it made him feel slightly dizzy.
Dulwich Picture gallery, which is run as a charity and receives no government funds, hopes to reach a new audience through its VR app, some of whom may end up travelling to see the museum first-hand.
The Dulwich Picture Gallery in London has become one of the first galleries in the UK to offer a virtual reality tour of its collection.