The 22-year-old suffered facial injuries after parting company with Lucky One in the Betway Mersey Novices' Hurdle at Aintree on Saturday. He was taken to hospital and it was expected he would make a quick recovery.
However, further checks revealing fractures in his cheekbone that will require surgery later this week, and he has been forced to end his campaign early.
Cobden currently sits in third in the jump jockeys' championship, 13 winners behind Harry Skelton and 14 adrift of defending champion Brian Hughes, with the duo locked in an enthralling battle that ends on April 24 at Sandown.
He tweeted: "I went for further scans yesterday and, unfortunately, they have shown that I have got a couple of fractures in my right cheekbone. I am having an operation on Thursday, but I am out for the rest of the season (likely to be six weeks).
"Good luck to both Brian and Harry in the champion jump jockey title race. I look forward to hopefully challenging you both again next season and I hope that next season also welcomes people back on to racecourses."