The Senegal international has seen limited action in recent weeks due to the issue, which Hull boss Steve Bruce had previously looked to manage with painkilling injections.
However, after further tests, Diame has been ordered to rest, and he is likely to be out for another month at the least.
A Hull statement read: "Diame has been troubled by the problem in recent weeks, missing the home game against Tottenham Hotspur last month before being withdrawn during the second half of the draw at Everton nearly a fortnight ago.
"After seeing a specialist late last week, the midfielder has been advised to wear a brace for a month and won't be back in action until 2015."
Diame enjoyed a fine start to his Hull career with four goals in his first five outings, although he has not managed to trouble the scorers in five subsequent outings.
Bruce is also sweating over the fitness of defender Michael Dawson, who limped out of Saturday's 2-0 defeat at Chelsea.
The Hull boss initially revealed he expected Dawson to miss six weeks of action, but the club revealed a more accurate timeframe would be determined by scans set for Monday.
