Media playback is not supported on this device
Dideriksen beat Dutch pre-race favourite Kirsten Wild in a sprint finish with Finland's Lotta Lepisto third on the 134.5km Qatar course.
Defending champion Deignan, 27, was sixth with one kilometre to go but did not have the power to retain her title.
Dideriksen, 20, is a double junior world champion.
Deignan - formerly Armitstead - had played down her chances in Doha, having focused her season on the hilly Olympic Games road race in Rio, where she finished fifth.
The men's race takes place on Sunday, with Mark Cavendish bidding for a second world title following his 2011 triumph in Copenhagen.
Britain's Lizzie Deignan finished fourth as Denmark's Amalie Dideriksen won the women's title at the Road World Championships in Doha.