Orudzhev, who was lying third in the championship following his second win of the season in the penultimate round at Austin, has not travelled to Sakhir as he is suffering from acute tonsillitis.
The SMP Racing driver has been replaced in the team by fellow Russian Konstantin Tereschenko, who was out of a drive going into this weekend because his regular team Teo Martin Motorsport had run into sponsorship problems.
In a statement posted on social media by the team, Orudzhev said: "I'm upset, this weekend I could have been competing for the championship.
"This means I also can't participate in the presentation of the new BR1 prototype [which is due to be launched on Friday evening], but now I need to stay in the hospital."
Before Bahrain, Orudzhev was 25 points behind championship leader Pietro Fittipaldi and 15 points behind his SMP team-mate Matevos Isaakyan with 50 points still available from the pair of races.
His illness means his third place is under threat as Force India Formula 1 development driver Alfonso Celis is just six points behind in fourth, with Rene Binder and Roy Nissany 24 points behind in fifth and sixth respectively.
The 2015 Formula Renault 3.5 season will be notable for being the last with the French company's backing but also produced a worthy champion in Oliver Rowland. PETER MILLS evaluates this year's crop of drivers
Last year's field was extraordinary and hard to match, but the Formula Renault 3.5 grid will still have plenty of talent this season. Glenn Freeman runs through the field ahead of this weekend's season opener
Landing the Fortec seat that took rising star Robin Frijns to the 2012 FR3.5 title was already a good sign for Stoffel Vandoorne. Then McLaren took him under its wing. Peter Mills tells Vandoorne's story so far