Dideriksen won a bunch sprint at the end of the 134-kilometres road race ahead of Holland’s Kirsten Wild on Saturday.
Lotta Lepisto of Finland was third and Deignan finished one place off the podium.
Deignan, nee Armitstead, won the world title in Richmond, Virginia in September 2015, fulfilling a life-long ambition.
The 27-year-old from Otley, a London 2012 silver medallist, had the honour of wearing the world champion’s rainbow jersey for the year. That honour now falls to Dideriksen.
Deignan had played down her chances in the pan-flat Doha route, having focused her season on the hilly Olympic Games road race in Rio.
But she was in the mix in the finale, only to fall narrowly short.
The men’s race takes place on Sunday’s final day of the eight-day event, with Mark Cavendish bidding for a second world title following his 2011 triumph in Copenhagen.