Grainger, who is chasing a record fifth Olympic medal in Rio, was fourth at the European Championships with Thornley.
Team performance director Sir David Tanner said: "After Lucerne, Katherine and Vicky will be given the opportunity to be considered for the eight."
Constantine Louloudis and Pete Reed also miss the event because of illness.
Louloudis has a virus and is replaced by Callum McBrierty in the men's four, who won gold at the European Championships earlier in May.
Reed has been struck down by the same illness and his place in the men's eight is taken by Alan Sinclair.
The women's eight won gold in Germany and are unchanged for the regatta on the Lake Rotsee in Switzerland, which will be a step up in class from the European Championships because many of the world's best crews will be racing.
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Britain's team for the Olympics is due to be finalised on 9 June, with the last regatta before Rio at the World Cup in Poznan on 17-19 June.
That date will also represent an opportunity for Kat Copeland and Charlotte Taylor to race again.
They failed to make the A final in the lightweight women's sculls in Brandenburg and have also been rested for the trip to Switzerland.
Elsewhere, Olympic, European and World champions Helen Glover and Heather Stanning will be aiming to continue their unbeaten run in the women's pair which stretches back to 2011.
Last year's world silver medallists Richard Chambers and Will Fletcher are in the lightweight men's double after they missed the European Championships because Chambers was recovering from injury.
Olympic champion Katherine Grainger and Vicky Thornley have been left out of the women's double at this weekend's World Cup regatta.