The 25-year-old only moved to Vicarage Road from West Ham at the end of last week, but had to be stretchered off just before half-time of the 1-1 draw with the Addicks.
Davenport was subsequently taken to hospital for x-rays, which showed up a broken bone in his neck.
Hornets boss Aidy Boothroyd had said straight after the game: "Calum heard a crack in his neck and he lost the sensation in his fingers and he is in the hospital now.
"When it is a neck injury you have to get him off the pitch straight away and we hope it is not too bad."