The vessel, which is registered in Samoa, was barred from returning there because the country is on lockdown as part of its Covid-19 precautions.
The boat sought permission to enter American Samoa so the injured fisherman could be treated, however it was denied because of fears surrounding the coronavirus.
However according to the Department of Health, a decision was made to provide medication for the man.
A vessel is to deliver the supplies to the boat.
The fishing boat, which is owned by one of the largest Taiwanese companies fishing in the region, has been waiting 32 kilometres out of harbour since the weekend.
A large hook is imbedded in the fisherman's arm and it's suspected the injury has become infected.
Local authorities say he could need surgery.