Manager Daniel Farke confirmed the news as he spoke ahead of the trip to Brighton & Hove Albion on Saturday.
"Yes, bad news," he said on Thursday. "Joe has a hamstring injury. He will be out for, at the moment, an assessment of eight to 10 weeks, so he will definitely not play before the next international break.
"Also, probably not the first games after the international break. A blow for us because he is a key player for us. But it is football and sometimes you have to deal also with injuries. He will definitely miss the next eight to 10 weeks."
Rodon has started in both of Leeds' league games so far.
His injury will also be a setback for Wales, who visit Portugal on September 24th and Denmark three days later in Nations League Group A4 matches in the next international break.
They also host Norway and Denmark in home Nations League games at the start of October.