He aggravated a groin injury while playing for Nigeria during this month's international break.
Awoniyi, signed from Union Berlin for a then club-record fee of 17 million pounds in 2022, has scored 15 goals in 39 games in all competitions for Forest in the last two seasons.
"It's bad news on Taiwo, he's had to have surgery and he is going to be out for months," Cooper told reporters ahead of Forest's home game against Brighton & Hove Albion on Saturday.
"He's become an important player for us with the goals he's scored and the goals he will score for us, but he's such a good guy and a good professional who is desperate to do well, so to get an injury like this is harsh on him.
"We've got to support him through the process of coming back stronger... We'll definitely see him again this season, but it's groin surgery so it will take a little while."
Forest are 14th in the table with 13 points from 12 games.
