Tuilaepa Sailele Malielegaoi, who is also chairman of the Samoa Rugby Union (SRU), made the comments in an interview with the Samoa Observer ahead of a local telephone fund-raising initiative.
"We are bankrupt," he said. "In other words we are insolvent. It means the Union cannot continue to pay off our debts with the banks. We also need money to pay the players so they can continue to play."
Samoa play Scotland at Murrayfield on Saturday and England at Twickenham on Nov. 25. Tuilaepa said there was no money to pay for player insurance and the head coach's salary.
Former Samoa international Daniel Leo said on Twitter that it was a "dark day for the rugby world".
Hosts are under no obligation to share gate receipts with visiting Test sides.
Sky Sports television reported, however, that the English Rugby Football Union (RFU) would compensate Samoa to the tune of about 75,000 pounds. All on-the-ground costs for visiting teams are also covered.
RFU chief executive Steve Brown told the BBC last month that the SRU had sought funding ahead of the tour and the English body would make a contribution.
The Samoa Observer in October quoted the SRU's annual report for 2016 as saying that the body was wrestling with a large overdraft after settling more than $1 million (£763,800) of debts in 2015.
"Overall activities of the Union for 2016 saw a net loss of $106,000 with the SRU posting a profit of $153,000 which was offset by a loss in High Performance Unit of $259,000," the report said.
"The Union’s immediate debts have decreased from $685,000 to $480,000 and the Union is looking at closing off all long outstanding debts by 2018."
(Reporting by Alan Baldwin, editing by Ken Ferris)