The 26-year-old Scotland international limped out of last Saturday's disappointing 0-0 Premier League draw with Crystal Palace with an ankle injury.
Both he and his manager are yet to discover the full extent of the damage to the same joint on which he had surgery last season, but he will play no part in Saturday's vital trip to Norwich and the Black Cats face an anxious wait until next week to discover whether or not his campaign has run its course.
Poyet said: "We are still assessing. I think next week, we are going to have the final decision on him, but he is not fit for this weekend and we are trying to see what we are going to do.
"It was quite swollen, so it's difficult to do all the tests. When you do the MRI tests, there is always some swelling around and it's not very, very clear, so we are trying to be calm and assess it properly next week."
Fletcher, a £12million signing from Wolves during the summer of 2012, was the club's leading scorer last season with 11 goals, has been hampered by fitness problems for much of the current campaign and has found the back of the net only three times to date.
However, with the Black Cats currently languishing inside the bottom three, Poyet would desperately like to have him available for the remaining 11 games as they try to fight their way to safety.
Asked if he feared losing the player for the remainder of the season, he said: "I hope not.
"It just depends on how bad the twist is, because definitely there was a twist. He jumped and he landed badly and he twisted his ankle.
"There is always the fear of if there are any bone issues, and there are not, that's for sure.
"But then there's the ligaments and depending how much they are damaged...
"But like I said, it's difficult to see, so we are keeping our fingers crossed and next week, we will have more news."
It has proved a depressing few months for the man in whom then manager Martin O'Neill invested so heavily, after a shoulder problem left him playing through the pain barrier in an effort to impress new boss Poyet.
The Uruguayan admitted Fletcher's season is not one he will remember with any great pleasure, although he is still hoping he can end it in positive fashion.
Poyet said: "I hope he finishes well. Who knows? Maybe we can have him for whatever games he plays at the end and keep himself fit and start well next year.
"It's been difficult for him. He has always come back - even before I got here the first injury, the shoulder, they were talking about three or four months, and he had a great recovery and he played a few games in real pain.
"But yes, it's probably a season to forget for him because personally, it's been quite difficult."