Morriston Hospital bosses issued an alert after a patient who died last month was found to have the virus.
Non-emergency cardiac surgery has been postponed at the hospital while an investigation is launched to discover the source of the infection.
All patients who had surgery at the hospital's cardiothoracic unit between March 11 and April 17 could potentially be infected. They are being offered blood tests to check whether they have contracted the virus.
Despite the concern, bosses at the ABM University Health Board, which runs the hospital, insist that the risk of infection is low.
The family of the female patient who died has since lodged an official complaint, which could lead to a medical negligence claim, after she was diagnosed as having an acute Hepatitis B infection.
The woman died after successfully undergoing surgery at the unit and being discharged from hospital after making a good recovery.
The investigation at the hospital has already ruled out staff and family members as a source of the infection.