It follows the decision of the Royal College of Art to turn regular venue Kensington Gore campus entirely over to academic use after a major refurbishment is completed in the summer.
Sister fair, the 20/21 International Art Fair, held in May for the ninth time, will also close.
Organiser Gay Hutson told ATG she would "look at alternative sites but, as we all know, venues for such events in central London are in very short supply".
The 20/21 fair has traditionally been a season opener, attracting both knowledgeable collectors and the art trade for whom it was a valuable buying ground before the autumn fairs season.
Keeping stand costs within the reach of smaller dealers in Modern British art has long been the event's priority.
A statement by Hutson and co-founder Bunny Wynn thanked all exhibitors "for their loyalty and support over the years. We should all be proud of what the fair has achieved in raising awareness of Modern British art."
Long-term 20/21 exhibitor Peter Osborne of Osborne Samuel, who sat on the fair's committee, said the event "managed to offer something to suit every pocket, which is a rare thing nowadays".
For months Hutson and Wynn have been negotiating with the RCA in a bid to keep the venue but it was decided the campus will no longer host commercial fairs.