The injury was sustained last weeks in the 2-1 victory over Doncaster Rovers, Otsemobor only lasted three minutes after pulling up with the injury and was stretchered off.
With Otsemobor out for a while an ideal opportunity has arisen for Crewe's latest signing Danny Woodards who was signed from Exeter City, boss Dario Gradi told the official site "It is a shame for Jon and for us - therefore, it is just as well we were able to sign Danny Woodards.
"He has done very well. As normally happens, one player's misfortune has been another player's opportunity."