The centre-back was forced off late in Sunday`s 1-0 win over Middlesbrough with a scan confirming the extent of the injury.
However, the damage is minimal and Monk could return in a fortnight.
The Swans are already without fellow defender Alan Tate for Saturday`s trip to Doncaster after he picked up his fifth booking of the campaign against Boro, automatically resulting in a one-match suspension.
Source: PA
Source: PA