Rashid underwent a scan on Tuesday and will now take some time out to rehabilitate his shoulder under England's medical team.
The 31-year-old, who helped England win the World Cup last month, told Yorkshireccc.com: "The aim was to come back after the World Cup and play for Yorkshire. I enjoy playing for Yorkshire, but it just wasn't meant to be.
"I’ve had a shoulder problem for a little while and I got through the World Cup with an injection. Obviously, as time has gone on the injection has worn out and, after the World Cup, I started feeling a bit of a pinch in my shoulder.
“These things can happen and fortunately it hasn’t happened to me earlier than it has. I’ve played 13-14 years of professional cricket and this is the first time I’ve suffered an injury to my shoulder.
“I’m very confident, after being ruled out for the rest of the season, that I can get myself fully fit before we go away in the winter. I’ve got two months now to get myself fully fit and it’s as simple as that."