Orlovsky has two fractures and a torn ligament in his right thumb. He will visit another specialist next week to determine whether he will need surgery. He
said he remains hopeful he will be able to return later in the season.
Culpepper, who was signed on Monday and has taken 80 percent of the snaps with the first-string offense this week, will start, according to ESPN.com's Chris Mortensen.
Second-year pro Drew Stanton is Marinelli's other option.
Marinelli also said center Dominic Raiola will miss Sunday's game with a broken right thumb, breaking his streak of 104 consecutive starts.
Senior writer John Clayton covers the NFL for ESPN.com. Information from The Associated Press and ESPN senior NFL analyst Chris Mortensen was used in this report.