The 28-year-old is undergoing treatment on the calf injury that forced him to miss the Robins' Championship defeat at QPR on Saturday.
Club physio Nick Dawes is hopeful that Williams will be fit when City resume league action at home to fellow play-off contenders Preston on April 4.
The news comes as a blow to Williams who had been in the international wilderness for three years since last being selected to represent his
country by then-manager Mark Hughes in 2005.
Wales' games against Finland and Germany are to be played at Cardiff's Millennium Stadium on March 28 and April 1 respectively.