The Boat Race Company says "the public good far outweighs all other considerations".
This year's event, scheduled for March 29, would have staged the 166th men's race and the 75th women's race between crews from Oxford and Cambridge universities.
A statement from The Boat Race Company Limited said: "As a result of the current situation with Covid-19, The Boat Race on March 29 has been cancelled. This decision is based entirely on our concern for the welfare of our crews, our spectators, our staff and volunteers."
The Boat Race Company Limited chairman Robert Gillespie added: "Given the unprecedented situation our country and each of us as individuals faces, the public good far outweighs all other considerations.
"Cancellation of The Boat Race is therefore clearly the correct decision, but it is not without sad consequence. Our thoughts are very much with the athletes who have worked so hard and made immense sacrifices to represent their University and are now unable to do so.
"To cancel is not an easy decision and we realise this news will undoubtedly disappoint all those who look forward to the Race each year - whether watching on the riverbanks, on TV or online.
"We would like to thank our partners, fans, the local businesses and community for their continued support."
Cambridge completed a second successive whitewash last year, with victories for the men and women - for the third successive year - and for both the men and women in the reserve races.