Wood has scored one goal in seven appearances since joining on loan from Newcastle United in the January transfer window.
The 31-year-old picked up a thigh injury within six minutes of coming on as a substitute in the 3-1 defeat to Tottenham Hotspur earlier this month.
Wood still travelled to meet up with the New Zealand national side, but he was unable to feature in either of the two friendlies against China.
Speaking ahead of Saturday's home meeting with Wolverhampton Wanderers, Cooper has now revealed that Wood sustained another injury issue on international duty, which will keep him out for the remainder of the season.
"Chris Wood is out for the season," Cooper told reporters. "He's picked up an injury during the international break."
There is further bad news as Serge Aurier, Andre Ayew and Gustavo Scarpa have also returned from the international period with injury issues.
Cooper said: "Serge, Andre and Gustavo have picked up some injuries over the break as well. We're not sure how long they will be out for or what their availability will be for the next few games."
Brennan Johnson was unable to meet up with the Wales squad due to a groin issue, and he remains a doubt for Saturday's contest.
"Brennan is not back to full fitness," Cooper added. "It's something we are assessing on a daily basis and are having to manage.
"Like some of the other guys, it's a little bit inconclusive at the moment, in terms of availability for the next games, with us having three in a week."
Despite having fitness concerns about several members of his squad, the Forest boss was able to provide some positive news.
"Taiwo (Awoniyi) and Cheikhou (Kouyate) are back in full training," Cooper said. "And obviously Moussa (Niakhate) is back now having played the last game and then making his international debut for Senegal - congratulations to him for that, I know what it means to him.
Forest head into the weekend in 16th position in the Premier League table with just two points separating them from the relegation zone.