The Sheffield Wednesday striker rejected a call-up to Alex McLeish's latest squad.
Fletcher wasn't named in Alex McLeish's squad for this month's Euro 2020 qualifiers against Kazakhstan and San Marino.
And the Wednesday top scorer has since revealed it was his decision not to join his Hillsborough teammate, Liam Palmer, in accepting the Tartan Army boss's call.
Fletcher has struggled with injuries in each of the last two campaigns and told Sheffield Wednesday's official website earlier he was concerned that playing on artificial surfaces could exacerbate those issues.
But speaking to BBC 606 on Sunday, Sutton said: "There's a lot of Scottish players who just simply don't want to play for Alex McLeish, seemingly.
"Steven Fletcher, you know, nursing a knee injury, apparently, but playing for Sheffield Wednesday. He shouldn't play again for Scotland."
Sutton, the former Celtic striker turned pundit, famously turned down a call-up to England's B team in the mid-1990s - something he expressed his regret at doing.
Fletcher has appeared twice for Sheffield Wednesday since rejecting McLeish's call and suffered a groin injury in the last of those - a 4-2 win against Blackburn Rovers.
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